56
Views
4
CrossRef citations to date
0
Altmetric
Original Articles

Chapter 6: linear preservers on numerical ranges, numerical radii and unitary similarity invariant norms

&
Pages 63-73 | Published online: 01 Apr 2008

References

  • Goldberg , M. 1979 . On certain finite dimensional numerical ranges and numerical radii . Linear and Multilinear Algebra , 1 : 329 – 342 .
  • Goldberg , M. and Straus , E. G. 1977 . Elementary inclusion relations for generalized numerical range . Linear Algebra Appl , 18 : 1 – 24 .
  • Goldberg , M. and Straus , E. G. 1979 . Norm properties of c-numerical radii . Linear Algebra Appl , 24 : 113 – 131 .
  • Halmos , P. R. 1967 . A Hilbert Space Problem Book , New York : von Nostrand .
  • Mathias , R. 1989 . “ A representation of unitary similarity invariant norms ” . In Technical report 515, Department of Mathematical Sciences , The Johns Hopkins University .
  • Beasley , L. B. 1970a . Linear operators on matrices:The invariance of the third elementary symmetric function . Can. J. Mam. , 22 : 746 – 752 .
  • Frobenius , G. 1897 . Uber die Darstellung der endlichen Gruppen durch Linear Substitutionen . S. B. Deutsch. Akad. Wiss. Berlin , 22 : 994 – 1015 .
  • Horn , R. A. and Johnson , C. R. 1991 . Topics on Matrix Analysis , Cambridge University Press .
  • Hu , S. and Tarn , T. Y. 1991a . Operators with permanent numerical ranges on straight lines . Linear and Multilinear Algebra , 29 : 263 – 278 .
  • Hu , S. and Tarn , T. Y. 1991b . On the generalized numerical range with principal character . Linear and Multilinear , 30 : 93 – 107 .
  • Johnson , C. C. R. and Pierce , S. 1985 . Linear maps on Hermitian matrices:The stabilizer of an inertia class . Can. Math. Bull , 28 : 401 – 404 .
  • Kovacs , A. 1976/1977 . Trace preserving linear transformations on matrix algebras . Linear and Multilinear Algebra , 4 : 243 – 250 .
  • Li , C. K. 1986 . “ Some Results on Generalized Spectral Radii ” . In Numerical Radii and Spectra Norms, Ph.D. Thesis , University of Hong Kong .
  • Li , C. K. 1987a . Linear operators preserving the numerical radius of matrices . Proc. of Amer. Math. Soc. , 99 : 601 – 608 .
  • Li , C. K. 1987b . Linear operators preserving the higher numerical radius of matrices . Linear and Multilinear , 21 : 63 – 73 .
  • Li , C. K. 1987c . “ Linear operators that preserve the m -numerical radius or the m -numerical range of matrices ” . In Current Trends in Matrix Theory , New York : North-Holland .
  • Li , C. K. , Tarn , B. S. and Tsing , N. K. 1988 . Linear operators preserving the (p,q) numerical range . Linear Algebra Appl , 110 : 75 – 89 .
  • Li , C. K. and Tsing , N. K. 1988a . Linear operators that preserve the c-numerical range or radius of matrices . Linear and Multilinear Algebra , 23 : 27 – 46 .
  • Li , C. K. and Tsing , N. K. 1988c . Linear operators preserving the decomposable numerical radius . Linear and Multilinear Algebra , 23 : 333 – 341 .
  • Li , C. K. and Tsing , N. K. 1988d . Duality between some linear preservers problems:The invariance of the C- . Linear and Multilinear Algebra , 23 : 353 – 362 .
  • Li , C. K. and Tsing , N. K. 1990c . Linear operators preserving unitary similarity invariant norms on matrices . Linear and Multilinear Algebra , 11 : 213 – 224 .
  • Man , W. Y. 1991 . The invariance of C-numericai range, C-numerical radius and their dual problems . Linear and Multilinear Algebra , 30 : 117 – 128 .
  • Marcus , M. 1959 . All linear operators leaving the unitary group invariant . Duke Math. J. , 26 : 155 – 163 .
  • Marcus , M. and Filippenko , I. 1979 . Linear operators preserving the decomposable numerical range . Linear and Multilinear Algebra , 7 : 27 – 36 .
  • Marcus , M. and Purves , R. 1959 . Linear transformations on algebras of matrices II:The invariance of the . Can. J. Math. , 11 : 383 – 396 .
  • Pellegrimi , V. J. 1975 . Numerical range preserving operators on a Banach algebra . Studia Math , 54 : 143 – 147 .
  • Pierce , S. and Watkins , W. 1978/1979 . Invariants of linear maps on matrix algebras . Linear and Multilinear Algebra , 6 : 185 – 200 .
  • Pierre , S. and Warkins , W. 1979 . Isometries of n2 . J. fur die Reine und Angew Math , 305 : 60 – 64 .
  • Schneider , H. 1965 . Positive operators and an inertia theorem . Numer Math. , 7 : 11 – 17 .
  • Tarn , T. Y. 1986 . “ A Study of Induced Operators on Symmetry Classes of Tensors ” . In Ph.D. Thesis , University of Hong Kong .
  • Tarn , T. Y. 1987a . Linear operators on matrices:The invariance of the decomposable numerical range . Linear Algebra Appl , 85 : 1 – 7 .
  • Tarn , T. Y. 1987b . Linear operators on matrices:The invariance of the decomposable numerical range . Linear Algebra Appl , 87 : 147 – 153 .
  • Tarn , T. Y. 1987c . Linear operators on matrices:The invariance of the decomposable numerical range . Linear Algebra Appl , 92 : 197 – 207 .
  • Tarn , T. Y. 1988 . On the numerical range of an induced power . Linear and Multilinear Algebra , 23 : 207 – 211 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.