Proceedings of the American Mathematical Society

			Journals Home Search Author Info Subscribe Tech Support My Subscriptions Help
ISSN 1088-6826(e) ISSN 0002-9939(p)

Completely rank nonincreasing linear maps on nest algebras

Author(s): Jinchuan Hou; Jianlian Cui
Journal: Proc. Amer. Math. Soc. 132 (2004), 1419-1428.
MSC (2000): Primary 47B48, 47L35
Posted: November 4, 2003
MathSciNet review: 2053348
Retrieve article in: PDF
This article is available free of charge

Abstract | References | Similar articles | Additional information

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:

1.: Chooi, W. and Lim, M., Linear preservers on triangular matrices, Linear Algebra Appl., 269 (1998), 241-255. MR 98m:15007
2.: Cui, J., Hou, J., and Li, B., Linear preservers on upper triangular operator matrix algebras, Linear Algebra Appl., 336 (2001), 29-50. MR 2002g:47074
3.: Davidson, K. R., Nest Algebras, Pitman Research Notes in Mathematics, Vol. 191, Longman Scientific and Technical, London/New York, 1988. MR 90f:47062
4.: Ge, L., Hadwin, D., Hou, J., and Li, J., Rank nonincreasing linear maps on operator spaces, preprint.
5.: Hadwin, D. and Larson, D., Completely rank nonincreasing linear maps, J. Funct. Anal., 199 (2003), 210-227.
6.: Hadwin, D. and Larson, D., Strong limits of similarities, Operator Theory: Advances and Applications, 104, Birkhäuser-Verlag, Basel, Switzerland, 1998, pp. 139-146. MR 99e:47040
7.: Hou, J., Rank-preserving linear maps on $\mathcal{B}(X)$ , Sci. China Ser. A 32 (1989), 929-940.MR 92b:47052
8.: Hou, J. and Cui, J., Rank-1 preserving linear maps on nest algebras, Linear Algebra Appl., 369 (2003), 263-277.
9.: Molnar, L. and Semrl, P., Some linear preserver problems on upper triangular matrices, Linear and Multilinear Algebra, 45 (1998), 189-206. MR 99h:15003
10.: Wei, S. and Hou, S., Rank preserving maps on nest algebras, J. Operator Theory, 39 (1998), 207-217.MR 2000m:47099

Similar Articles:

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 47B48, 47L35

Retrieve articles in all Journals with MSC (2000): 47B48, 47L35

Additional 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

DOI: 10.1090/S0002-9939-03-07275-7
PII: S 0002-9939(03)07275-7
Keywords: Nest algebras, rank, linear maps
Received by editor(s): October 8, 2001
Received by editor(s) in revised form: January 8, 2003
Posted: November 4, 2003
Additional Notes: This work is supported by NNSFC and PNSFS
Communicated by: David R. Larson
Copyright of article: Copyright 2003, American Mathematical Society

	Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
\|