Completely rank nonincreasing linear maps on nest algebras
HTML articles powered by AMS MathViewer
- by Jinchuan Hou and Jianlian Cui
- Proc. Amer. Math. Soc. 132 (2004), 1419-1428
- DOI: https://doi.org/10.1090/S0002-9939-03-07275-7
- Published electronically: November 4, 2003
- PDF | Request permission
Abstract:
In this paper, the completely rank nonincreasing bounded linear maps on nest algebras acting on separable Hilbert spaces are characterized, and an affirmative answer to a problem posed by Hadwin and Larson is given for the case of such nest algebras.References
- W. L. Chooi and M. H. Lim, Linear preservers on triangular matrices, Linear Algebra Appl. 269 (1998), 241–255. MR 1483531, DOI 10.1016/S0024-3795(97)00069-4
- Jianlian Cui, Jinchuan Hou, and Bingren Li, Linear preservers on upper triangular operator matrix algebras, Linear Algebra Appl. 336 (2001), 29–50. MR 1855390, DOI 10.1016/S0024-3795(01)00288-9
- Kenneth R. Davidson, Nest algebras, Pitman Research Notes in Mathematics Series, vol. 191, Longman Scientific & Technical, Harlow; copublished in the United States with John Wiley & Sons, Inc., New York, 1988. Triangular forms for operator algebras on Hilbert space. MR 972978
- Ge, L., Hadwin, D., Hou, J., and Li, J., Rank nonincreasing linear maps on operator spaces, preprint.
- Hadwin, D. and Larson, D., Completely rank nonincreasing linear maps, J. Funct. Anal., 199 (2003), 210–227.
- Donald W. Hadwin and David R. Larson, Strong limits of similarities, Nonselfadjoint operator algebras, operator theory, and related topics, Oper. Theory Adv. Appl., vol. 104, Birkhäuser, Basel, 1998, pp. 139–146. MR 1639652
- Jin Chuan Hou, Rank-preserving linear maps on $B(X)$, Sci. China Ser. A 32 (1989), no. 8, 929–940. MR 1055310
- Hou, J. and Cui, J., Rank-1 preserving linear maps on nest algebras, Linear Algebra Appl., 369 (2003), 263-277.
- Lajos Molnár and Peter emrl, Some linear preserver problems on upper triangular matrices, Linear and Multilinear Algebra 45 (1998), no. 2-3, 189–206. MR 1671619, DOI 10.1080/03081089808818586
- Shu-Yun Wei and Sheng-Zhao Hou, Rank preserving maps on nest algebras, J. Operator Theory 39 (1998), no. 2, 207–217. MR 1620558
Bibliographic Information
- Jinchuan Hou
- Affiliation: Department of Mathematics, Shanxi Teachers University, Linfen, 041004, People’s Republic of China
- Address at time of publication: Department of Mathematics, Shanxi University, Taiyuan 030000, People’s Republic of China
- Email: jhou@dns.sxtu.edu.cn
- Jianlian Cui
- Affiliation: School of Mathematical Sciences, Peking University, Beijing 100871, People’s Republic of China
- Address at time of publication: Department of Mathematics, Shanxi Teachers University, Linfen, 041004, People’s Republic of China
- Email: cuijl@dns.sxtu.edu.cn
- Received by editor(s): October 8, 2001
- Received by editor(s) in revised form: January 8, 2003
- Published electronically: November 4, 2003
- Additional Notes: This work is supported by NNSFC and PNSFS
- Communicated by: David R. Larson
- © Copyright 2003 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 132 (2004), 1419-1428
- MSC (2000): Primary 47B48, 47L35
- DOI: https://doi.org/10.1090/S0002-9939-03-07275-7
- MathSciNet review: 2053348