Invertible preservers and algebraic groups III: Preservers of unitary similarity (congruence) invariants and overgroups of some unitary subgroups

Linear and Multilinear Algebra

Volumn 43, Issue 1-3, 1997, Pages 257-282

  Guralnick, Robert M ^a   Li, Chi Kwong ^b  

^a UNIVERSITY OF SOUTHERN CALIFORNIA   (United States)

^b The College of William and Mary   (United States)

Author keywords

Linear preserver; Unitary group; Unitary similarity orbit

Indexed keywords

EID: 21944447767     PISSN: 03081087     EISSN: None     Source Type: Journal    
DOI: 10.1080/03081089708818528     Document Type: Article

References (37)

1. [AL] Ando, T. and Li, C. K. (editors), (1994). The numerical range and numerical radius, Linear and Multilinear Algebra, 37, 1-238.
2. [BL] Bebiano, N. and Li, C. K. (1992). A brief survey on the decomposable numerical range of matrices, Linear and Multilinear Algebra, 32, 179-190.
3. [BLP] Bebiano, N., Li, C. K. and da Providencia, J. (1993). Some results on the numerical range of derivations, SIAM J. Matrix Anal. Appl., 14, 1084-1095.
4. [BS] Brǎer, M. and Sěmrl, P. (1994). Normal-preserving linear mappings, Canad. Math. Bull., 37, 306-309.
5. Choi, M. D. et al. (1987). On the congruence numerical ranges and related functions of matrices, Linear and Multilinear Algebra, 22, 1-5.
6. Dixon, J. (1977). Rigid embeddings of simple groups in the general linear group, Canad. J. Math., 29, 384-391.
7. Doković, D. Z. and Li, C. K. (1994). Overgroups of some classical groups with applications to linear preserver problems, Linear Algebra Appl., 197-198, 31 - 62.
8. [DP] Doković, D. Z. and Platonov, V.P. (1993). Algebraic groups and linear preserver problems, C.R. Acad. Sci. Paris, 317, 925-930.
9. [Dy] Dynkin, E. (1957). Maximal subgroups of the classical groups, Amer. Math. Soc. Trans., 6, 245-378.
10. [Go] Goto, M. (1969). On an arcwise connected subgroup of a Lie group, Proc. Amer. Math. Soc., 20, 157-162.
11. [G1] Guralnick, R. M. (1994). Invertible preservers and algebraic groups, Linear Algebra Appl., 212/213, 249-257.
12. n(double struck F sign), Linear and Multilinear Algebra, to appear.
13. [KH] Kunicki, C. M. and Hill, R. D. (1992). Normal-preserving linear transformations, Linear Algebra Appl., 170, 107-115.
14. [HJ] Horn, R. A. and Johnson, C. R. (1991). Topics in Matrix Analysis, Cambridge Univ. Press, New York.
15. [HLT] Horn, R. A., Li, C. K. and Tsing.N. K. (1991). Linear operators preserving certain equivalence relations on matrices, SIAM J. Matrix Anal. Appl., 12, 195-204.
16. [HT1] Hu, S. A. and Tam, T. Y. (1991). Operators with permanental numerical ranges on a straight line, Linear and Multilinear Algebra, 29, 263-277.
17. [HT2] Hu, S. A. and Tam, T. Y. (1991). On the generalized numerical ranges with principal character, Linear and Multilinear Algebra, 30, 93-107.
18. [L1] Li, C. K. (1994). A class of linear preserver problems and some useful approaches, Linear Algebra Appl., 197-198, 817-824.
19. [L2] Li, C. K. (1994). C-numerical ranges and C-numerical radii, Linear and Multilinear Algebra, 37, 51-82.
20. [L3] Li, C. K. (1994). Linear operators preserving the (p, q) numerical radius, Linear Algebra Appl., 201, 21-42.
21. [LMR] Li, C. K., Mehta, P.P. and Rodman, L. (1994). A generalized numerical range: The range of a constrained sesquilinear form, Linear and Multilinear Algebra, 37, 25-50.
22. [LM] Li, C. K. and Merino, D. (1993). Linear operators preserving unitary t-congruence (orthogonal similarity) on complex (real) matrices, Linear and Multilinear Algebra, 35, 83-106.
23. [LP] Li, C. K. and Pierce, S. (1994). Linear operators preserving similarity classes and related results, Canad. Math. Bull., 37, 374-383.
24. [LT1] Li, C. K. and Tsing, N. K. (1988). Duality between some linear preserver problems: The invariance of the C-numerical range, the C-numerical radius and certain matrix sets, Linear and Multilinear Algebra, 23, 353-362.
25. [LT2] Li, C. K. and Tsing, N. K. (1990). Linear operators preserving unitary similarity invariant norms on matrices, Linear and Multilinear Algebra, 21, 213-224.
26. [LT3] Li, C. K. and Tsing, N. K. (1990). Duality between some linear preserver problems III: c-spectral norms on (skew) symmetric matrices and matrices with fixed singular values, Linear Algebra Appl. 67-97.
27. [LT4] Li, C. K. and Tsing, N. K. (1992). Linear preserver problems: A brief introduction and some special techniques, Linear Algebra Appl., 162-164, 217-236.
28. [Lk1] Liebeck, M. W. (1985). On the orders of the maximal subgroups of the finite classical groups, Proc. London Math. Soc., 50, 426-446.
29. [1K2] Liebeck, M. W. (1987). The affine permutation groups of rank three, Proc. London Math. Soc., 54, 477-516.
30. Man, W. Y. (1991). The invariance of C-numerical range, C-numerical radius and their dual problem, Linear and Multilinear Algebra, 30, 117-128.
31. [Ma] Marcus, M. (1973). Finite Dimensional Multilinear Algebra, Part I, Marcel Dekker, New York.
32. [OV] Onishchik, A. L. and Vinberg, E. B. (1990). Lie Groups and Algebraic Groups, Springer-Verlag, New York.
33. [P] Pierce, S. et al. (1992). A survey of Linear Preserver Problems, Linear and Multilinear Algebra, 33, 1-130.
34. [PW] Piercem, S. and Watkins, W. (1978/79). Invariants of linear maps on matrix algebras, Linear and Multilinear Algebra, 6, 185-200.
35. [PD1] Platonov, V. P. and Dokovic̀, D. Z. Linear preserver problems and algebraic groups, Preprint 94-029, Discrete Structures in Math., University of Bielefeld.
36. 2,ℂ) containing PSU(n), Trans. Amer. Math. Soc., 348, 141-152.
37. Varadarajan, V. S. (1971). Lie Groups, Lie Algebras and Their Representations, Prentice-Hall, Englewood Cliffs, N. J.