Emeritus Professor Pei Yuan Wu

Contact

• Email: pywu@math.nctu.edu.tw
• Tel: +886-3-571-2121 ext. 56426
• Fax: +886-3-572-4679
• Address: Department of Applied Mathematics, National Chiao Tung University,1001 Ta Hsueh Road, Hsinchu, Taiwan 30010, ROC

Teaching

• Fall Semester, 2024：
• Spring Semester, 2025：

Vitae

• Education
  • National Taiwan University (1965-1969) B.S. (Taipei, Taiwan)
  • Indiana University (1970-1975) Ph.D. (Bloomington, Indiana,USA)
• Research Areas
  • Operator Theory
  • Functional Analysis
  • Matrix Analysis
• Positions, Honors and Awards
  • Associate Instructor, Indiana University, Sept., 1970 - Dec., 1974
  • Lecturer, The University of Michigan - Flint, Jan., 1975 - April, 1975
  • Associate Professor, National Chiao Tung University, August, 1975 - July, 1978
  • Visiting Assistant Professor, Indiana University, June, 1976 - August, 1976
  • Professor, National Chiao Tung University, August, 1978 - February2014
  • Visiting Scholar, Indiana University, August, 1979 - July, 1980
  • Chairman, Dept. of Applied Mathematics, National Chiao Tung University, August, 1980 - Jan., 1982
  • Visiting Scholar, University of Toronto, Sept., 1987 - August, 1988
  • Visiting Research Associate, Dalhousie University, Sept., 1993 - Dec., 1993
  • Visiting Scholar, University of Toronto, Jan., 1994 - August, 1994
  • Recipient, Travel Grants from IMU Fund for Young Mathematicians to ICM - 78 at Helsinki
  • Best Teaching Award, National Chiao Tung University (1984)
  • Shou-Keng Chuang Science Award, Shou-Keng Chuang Public Interest Foundation (1984)
  • Outstanding Research Award, National Science Council of the Republic of China (1985 & 1987)
  • Science Prize, Education Ministry of the Republic of China (1989)
  • Chair Professorship, National Chiao Tung University (2006-2008, 2008-2010)
  • LifeTime Chair Professorship, National Chiao Tung University (2010-2014)
  • Professor Emeritus, National Chiao Tung University (April, 2014- present)
  • Editor, Bulletin of the Institute of Mathematics Academia Sinica (1985 - 2005)
  • Editor, Chinese Journal of Mathematics (1985 - 1996)
  • Editor, Taiwanese Journal of Mathematics (1997 - 2003)
  • Editor-in-chief, Taiwanese Journal of Mathematics (1998-2000)
  • Editor, Proceedings of the National Science Council, Republic of China, Part A: Physical Science and Engineering (2000–2001)
  • Reviewer, Zentralblatt fur Mathematik (1979 - 2013)
  • Reviewer, Mathematical Reviews (1995 - 2013)
  • Plenary speaker, the 12th International Linear Algebra Society Conference, June 29, 2005,
  • Regina, Saskatchewan, Canada Member of Scientific Organizing Committee, the 14th International Linear Algebra Society Conference, 2007,
  • Shanghai, China Guest editor, Special issue of Linear Algebra and its Applications for the 14th International Linear Algebra Society Conference, 430 (5-6) (2009), 1441-1724
  • Editor, Operators and Matrices (2007 - 2015)
  • Editor, International Journal of Mathematics and Mathematical Sciences (2009-2015)
  • Editor, Banach Journal of Mathematical Analysis (2013 - 2015)
• Recent Research Projects
  • Numerical Ranges of Bounded Operators (96-2115-M-009-013-MY3)
  • A Study of Numerical Ranges of Finite Matrices and Operators (99-2115-M-009-002-MY2)
  • Numerical Ranges of Tensor Products (101-2115-M-009-004)
  • Numerical Ranges of KMS matrices (102-2115-M-009-007)
• Student Supervision
  • Kung-Hwang Kuo, Ph.D., 1990, "Products of orthogonal projections and related topics"
  • Kung-Yeu Chen, Ph.D., 1991, "Quasinormal operators: Similarity, quasisimilarity and compact perturbation"
  • Jin-Hsien Wang, Ph.D., 1991, "Decomposition of operators into quadratic types"
  • Chii-Huei Yu, Ph.D., 1997, "A study on sums of idempotents"
  • Hwa-Long Gau, Ph.D., 1998, "Numerical ranges of S(Φ) "
  • Ching-I Hsin, Ph.D., 1999, "Operators similar to irreducible ones"
  • Ming Cheng Tsai, Ph.D., 2011, " A study of numerical ranges of operators and matrices”
  • Hisn-Yi Lee, Ph.D., 2014, "Gau-Wu numbers of certain matrices"

Selected Publications

(A)   Refereed Papers：

1. On nonorthogonal decompositions of certain contractions, Acta Sci. Math. (Szeged), 37 (1975), 301-306.
2. Commutants of C0(N) contractions, Acta Sci.Math.(Szeged), 38 (1976), 193-202.
3. The splitting of a(T1⊕T2) and related questions, Indiana Univ. Math. J., 26 (1977), 41-56 (jointly with John B. Conway).
4. On contractions satisfying Alg T=(T)', Proc. Amer. Math. Soc., 67 (1977), 260-264.
5. Quasi-similarity of weak contractions, Proc. Amer. Math. Soc., 69 (1978), 277- 282.
6. Hyperinvariant subspaces of the direct sum of certain contractions, Indiana Univ. Math. J., 27 (1978), 267-274; erratum, Indiana Univ. Math. J., 28 (1979), 699.
7. Jordan model for weak contractions, Acta Sci. Math. (Szeged), 40 (1978), 189-196.
8. Hyperinvariant subspaces of C11contractions, II, Indiana Univ. Math. J., 27 (1978), 805-812.
9. The hyperinvariant subspace lattice of a contraction of class C.0, Proc. Amer. Math. Soc., 72 (1978), 527-530.
10. Conditions for completely nonunitary contractions to be spectral, J. Func. Anal., 31(1979), 1-12.
11. Hyperinvariant subspaces of C11 contractions, Proc. Amer. Math. Soc., 75 (1979), 53-58.
12. Hyperinvariant subspaces of weak contractions, Acta Sci. Math. (Szeged), 41 (1979), 259-266.
13. Bi-invariant subspaces of weak contractions, J. Operator Theory, 1 (1979), 261- 272.
14. C11 contractions are reflexive, Proc. Amer. Math. Soc., 77 (1979), 68-72.
15. On the weakly closed algebra generated by a weak contraction, J. Operator Theory, 2 (1979), 141-148.
16. On contractions of class C1., Acta Sci. Math. (Szeged), 42 (1980), 205-210.
17. On the reflexivity of C0 (N) contractions, Proc. Amer. Math. Soc., 79 (1980), 405-409.
18. On a conjecture of Sz.-Nagy and Foias, Acta Sci. Math. (Szeged), 42 (1980), 331-338.
19. On the quasi-similarity of hyponormal contractions, Illinois J. Math., 25 (1981), 499-503.
20. C.0 contractions: cyclic vectors, commutants and Jordan models, J. Operator Theory, 5 (1981), 53-62.
21. C11 contractions are reflexive. II, Proc. Amer. Math. Soc., 82 (1981), 226-230.
22. The structure of quasinormal operators and the double commutant property, Trans. Amer. Math. Soc., 270 (1982), 641-657 (jointly with John B. Conway).
23. Approximate decompositions of certain contractions, Acta Sci. Math. (Szeged), 14 (1982), 137-149.
24. When is a contraction quasi-similar to an isometry?, Acta Sci. Math. (Szeged), 44 (1982), 151-155.
25. On the reflexivity of C1. contractions and weak contractions, J. Operator Theory, 8 (1982), 209-217.
26. Reflexivity and double commutant porperty for hyponormal contractions, Rev. Roum. Math. Pures Appl., 28 (1983), 631-635.
27. Multiplicities of isometries, Integral Equations Operator Theory, 7 (1984), 436- 439.
28. Which C.0 contraction is quasi-similar to its Jordan model?, Acta Sci. Math. (Szeged), 47 (1984), 449-455.
29. Contractions with constant characteristic function are reflexive, J. London Math. Soc., 29 (1984), 533-544.
30. Contractions with a unilateral shift summand are reflexive, Integral Equations Operator Theory, 7 (1984), 899-904.
31. Toward a characterization of reflexive contractions, J. Operator Theory, 13 (1985), 73-86.
32. Hyponormal operators quasisimilar to an isometry, Trans. Amer. Math. Soc., 291 (1985), 229-239.
33. Approximation by partial isometries, Proc. Edinburgh Math. Soc., 29 (1986), 255-261.
34. Products of nilpotent matrices, Linear Algebra Appl., 96 (1987), 227-232.
35. Products of positive semidefinite matrices, Linear Algebra Appl., 111 (1988), 53-61.
36. Products of normal operators, Canad. J. Math., 40 (1988), 1322-1330.
37. Contractions quasisimilar to an isometry, Acta Sci. Math. (Szeged), 53 (1989), 139-145.
38. Approximation by invertible and noninvertible operators, J. Approximation Theory, 56 (1989), 267-276.
39. The operator factorization problems, Linear Algebra Appl., 117 (1989), 35-63.
40. Factorization of matrices into partial isometries, Proc. Amer. Math. Soc., 105 (1989), 263-272 (jointly with K.-H. Kuo).
41. Convex combinations of projections, Linear Algebra Appl., 136 (1990), 25-42 (jointly with M.-D. Choi).
42. Sums of idempotent matrices, Linear Algrebra Appl., 142 (1990), 43-54.
43. Products of unipotent matrices of index 2, Linear Algrbra Appl., 149 (1991), 111-123 (jointly with J.-H. Wang).
44. Sums of square-zero operators, Studia Math., 99 (1991), 115-127 (jointly with J.-H. Wang).
45. Products of orthogonal projections, "Functional Analysis and Related Topics", S. Koshi, ed., World Scientific, Singapore, 1991, pp. 127-137 (jointly with K.-H. Kuo).
46. Similarity and quasisimilarity of quasinormal operators, J. Operator Theory, 27 (1992), 385-412 (jointly with K.-Y. Chen and D. A. Herrero).
47. All (?) about quasinormal operators, "Operator Theory and Complex Analysis", T. Ando & I. Gohberg, eds., Operator Theory: Advances and Applications, Vol. 59, Birkhuser Verlag, Basel, 1992, pp. 372-398.
48. Which linear transformations have isomorphic hyperinvariant subspace lattices?, Linear Algrbra Appl., 169 (1992), 163-178.
49. Products of diagonal operators, Chinese Sci. Bull., 38 (1993), 265-268 (jointly with J.-C. Hou, M.-C. Gao & X.-L. Zhang).
50. Diagonal operators: dilation, sum and product, Acta Sci. Math. (Szeged), 57 (1993), 125-138 (jointly with C. K. Fong).
51. Additive combinations of special operators, "Functional Analysis and Operator Theory", J. Zemnek, ed., Banach Center Pub., Vol. 30, Warsaw, Poland, (1994), pp. 337-361.
52. Sums and products of cyclic operators, Proc. Amer. Math. Soc., 122 (1994), 1053-1063.
53. Difference and similarity models of two idempotent operators, Linear Algebra Appl., 208/209 (1994), 257-282 (jointly with J.-H. Wang).
54. Band-diagonal operators, Linear Algebra Appl., 248 (1996), 185-204 (jointly with C. K. Fong).
55. Diagonal unitary dilations of contractions, Proc. Intern. Math. Conf.'94, World Scientific, Singapore, (1996), pp. 219-226.
56. Unitary dilations and numerical ranges, J. Operator Theory, 38 (1997), 25-42.
57. A numerical range characterization of Jordan blocks, Linear Multilinear Algebra, 43(1998), 351-361.
58. Sums of strongly irreducible operators, Houston J. Math., 24 (1998), 467-481 (jointly with C.-L. Jiang).
59. Dilation to the unilateral shifts, Integral Equations Operator Theory., 32 (1998), 101-113 (jointly with K. Takahashi).
60. Numerical range of S(ψ), Linear Multilinear Algebra, 45 (1998), 49-74 (jointly with H.-L. Gau).
61. Dilation to inflations of S(ψ), Linear Multilinear Algebra, 45 (1998), 109-123 (jointly with H.-L. Gau).
62. Matricial ranges of quadratic operators, Rocky Mountain J. Math., 29 (1999), 1139-1152 (jointly with S.-H. Tso).
63. Singular unitary dilations, Integral Equations Operator Theory, 33 (1999), 231-247 (jointly with K. Takahashi).
64. Lucas’ theorem refined, Linear Multilinear Algebra, 45 (1999), 359-373 (jointly with H.-L. Gau).
65. Polygons and numerical ranges, Amer. Math. Monthly, 107 (2000), 528-540.
66. The numerical range of a nonnegative matrix, Linear Algebra Appl.,350 (2002),1-23 (jointly with C.-K. Li and B.-S. Tam).
67. Numerical range of Aluthge transform of operator, Linear Algebra Appl., 357 (2002), 295-298.
68. Higher-dimensional numerical ranges of quadratic operators, J. Operator Theory, 49 (2003), 153-171 (jointly with M.-T. Chien & S.-H. Tso).
69. Direct sums of irreducible operators, Studia Math., 155 (2003), 37-49 (jointly with J. S. Fang & C.-L. Jiang).
70. Condition for the numerical range to contain an elliptic disc, Linear Algebra Appl. 364 (2003), 213-222 (jointly with H,-L. Gau).
71. Finite Blaschke products of contractions, Linear Algebra Appl., 368 (2003), 359-370 (jointly with H.-L. Gau).
72. Numerical range and Poncelet property, Taiwanese J. Math., 7 (2003) 173-193 (jointly with H.-L. Gau).
73. Numerical range of a normal compression, Linear Multilinear Algebra, 52 (2004), 195-201 (jointly with H.-L. Gau).
74. Companion matrices: reducibility, numerical range and similarity to contractions, Linear Algebra Appl., 383 (2004), 127-142 (jointly with H.-L. Gau).
75. Numerical range circumscribed by two polygons, Linear Algebra Appl., 382 (2004), 155-170 (jointly with H.-L. Gau).
76. Numerical range of a normal compression II, Linear Algebra Appl., 390 (2004), 121-136 (jointly with H.-L. Gau).
77. Anderson’s theorem for compact operators, Proc. Amer. Math. Soc., 134 (2006), 3159 - 3162 (jointly with H.-L. Gau).
78. Finite-rank perturbations of positive operators and isometries, Studia Math., 173 (2006), 73-79 (jointly with M.-D. Choi).
79. Polar decompositions of contractions, Integral Equations Operator Theory, 56 (2006), 559-569.
80. Numerical ranges of companion matrices, Linear Algebra Appl., 421 (2007), 202-218 (jointly with H.-L. Gau).
81. Line segments and elliptic arcs on the boundary of a numerical range, Linear Multilinear Algebra, 56 (2008), 131 - 142 (jointly with H.-L. Gau).
82. Higher-rank numerical ranges and dilations, J. Operator Theory, 63 (2010), 181-189 (jointly with H.-L. Gau and C.-K. Li).
83. Fredholmness of linear combinations of two idempotents, Integral Equations Operator Theory, 59 (2007), 579-583 (jointly with H.-L. Gau).
84. Numerical radius inequality for C0 contractions, Linear Algebra Appl., 430 (2009), 1509-1516 (jointly with H.-L. Gau and M. C. Tsai).
85. Numerical radius inequalities for square-zero and idempotent operators, Oper. Matrices, 2 (2008), 137-141 (jointly with H.-L. Gau and C.-Y. Huang).
86. Numerical ranges of nilpotent operators, Linear Algebra Appl., 429 (2008), 716-726 (jointly with H.-L. Gau).
87. Inner functions of numerical contractions, Linear Algebra Appl., 430 (2009), 2182-2191 (jointly with H.-L. Gau).
88. Numerical ranges of radial Toeplitz operators on Bergman space, Integral Equations Operator Theory, 65 (2009), 581-591 (jointly with K.-Z. Wang).
89. Unitary part of a contraction, J. Math. Anal. Appl., 366 (2010), 700-705 (jointly with H.-L. Gau).
90. Defect indices of powers of a contraction, Linear Algebra Appl., 432 (2010), 2824-2833 (jointly with H.-L. Gau).
91. Crawford numbers of powers of a matrix, Linear Algebra Appl., 433 (2010), 2243-2254 (jointly with K.-Z Wang and H.-L. Gau).
92. Numerical ranges of weighted shift matrices, Linear Algebra Appl., 435 (2011), 243-254 (jointly with M.C. Tsai).
93. Numerical ranges of weighted shifts, J. Math. Anal. Appl., 381 (2011), 897-909 (jointly with K.-Z. Wang.)
94. Numerical ranges as circular discs, Applied Math. Lett., 24 (2011), 2115-2117.
95. Noncircular elliptic discs as numerical ranges of nilpotent operators, Linear Multilinear Algebra, 60 (2012),1225-1233 (jointly with H.-L. Gau).
96. Numerical ranges and Geršgorin discs, Linear Algebra Appl., 438 (2013), 1170-1192. (jointly with C.-L. Chang, H.-L. Gau & K.-Z. Wang).
97. Numerical ranges and compressions of Sn-matrices,Oper. Matrices, 7 (2013), 465-476  (jointly with H.-L. Gau).
98. Diagonals and numerical ranges of weighted shift matrices, Linear Algebra Appl., 438 (2013), 514-532 (jointly with K.-Z. Wang).
99. Higher-rank numerical ranges and Kippenhahn polynomials, Linear Algebra Appl., 438 (2013), 3054-3061 (jointly with H.-L. Gau)
100. Numerical ranges of KMS matrices, Acta Sci. Math. (Szeged), 79 (2013), 583-610 (jointly with H.-L. Gau).
101. Zero-dilation indices of KMS matrices, Ann. Funct. Anal., 5 (2014), 30-35 (jointly with H.-L. Gau).
102. Numerical radii for tensor products of matrices, Linear Multilinear Algebra, 63 (2015)，1916-1936 (jointly with H.-L. Gau & K.-Z. Wang).
103. Numerical radii for tensor products of operators, Integral Equations Operator Theory, 78 (2014(, 375-382 (jointly with H.-L. Gau & K.-Z. Wang).
104. Zero-dilation index of a finite matrix, Linear Algebra Appl., 440 (2014), 111 - 124 (jointly with H.- L. Gau & K. -Z. Wang).
105. Structures and numerical ranges of power partial isometries, Linear Algebra Appl., 440 (2014), 325-341 (jointly with H.- L. Gau).
106. Sums of orthogonal projections, J. Func. Anal., 267 (2014), 384-404 (jointly with M.-D. Choi)
107. Power partial isometry index and ascent of a finite matrix, Linear Algebra Appl., 459 (2014), 136-144 (jointly with H. - L. Gau).
108. Excursions in numerical ranges,  Bull. Inst. Math. Acad. Sin. (N. S.),9 (2014), 351-370 (jointly with H. -L. Gau).
109. Upper and lower bounds for numerical radii of block shibts, Bull. Iraniam Math. Soc., accepted (jointly with  H. - L. Gau)
110. Circular numerical ranges of partial isometries, Linear Multilinear Algebra, accepted (jointly with  H. - L. & Gau  K.-Z. Wang)
111. Cramford numbers of companion matices, Open Matrices, accepted (jointly with  H. - L. & Gau  K.-Z. Wang)

(B)   Conference Papers：

1. Dilation to unilateral shifts, “Semigroups of Operators: Theory and Applications”, A. V. Balakrishnan, ed., Progress in Nonlinear Differential Equations and Their Applications, Vol. 42, Birkhauser Verlag, Basel, 2000, pp. 364-367.
2. Direct sums of irreducible operators, Trends in Mathematics, 2(1999), 40-44.
3. Numerical ranges of compressions of the shifts, “Semigroups of Operators: Theory and Applications”, C. Kubrusly, N. Levan & M. da Silveira, eds., Optimization Software, Los Angeles, 2002, pp.351-356.

(C)   Others：

1. Review of Hari Bercovici's Operator theory andAarithmetic in H∞, Bull. Amer. Math. Soc. (New Series), 21(1989), 184-186.
2. Multiplicative commutator and product of involution, "Linear and Complex Analysis Problem Book 3, Part I", V. P. Havin & N. K. Nikolski, eds., Lecture Notes in Math., No. 1573, Springer-Verlag, Berlin, 1994, pp. 229-230.
3. Products of two normal operators, preprint (jointly with M.-D. Choi).
4. Matrix interpretation of Marden’s proof of Siebeck’s theorem, preprint (jointly with B. Mirman).
5. Numerical Ranges of Hilbert Space Operators, manuscript, 327 pages.

go back