RANK-PRESERVING LINEAR MAPS ON B(X)

被引：0

作者：

侯晋川

机构：

[1] Linfen

[2] Shanxi Teachers University

[3] Department of Mathematics

来源：

Science China Mathematics | 1989年 / 08期

关键词：

Banach space; linear operator; elementary operator; rank of operator spectrum;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

Denote by B(X) the Banach algebra of all bounded linear operators on a complex Banach space X. In this paper, the representation of weakly continuous linear maps on B(X) which maps rank-1 operators to operators of rank at most 1 is given, and sequentially, some representation theorems for rank-preserving linear maps, spectrum-preserving linear maps and positivity-preserving linear maps on B(X) are obtained.

引用

页码：929 / 940

页数：12

共 50 条

[31] Nonlinear maps preserving similarity on B(X)
Qin, Zijie
Chen, Chaoqun
LINEAR & MULTILINEAR ALGEBRA, 2023, 71 (03): : 363 - 376
[32] Maps preserving Lie product on B(X)
Yu, Xiuping
Lu, Fangyan
TAIWANESE JOURNAL OF MATHEMATICS, 2008, 12 (03): : 793 - 806
[33] In the pursuit of sparseness: A new rank-preserving penalty for a finite mixture of factor analyzers
Kim, Nam-Hwui
Browne, Ryan P.
COMPUTATIONAL STATISTICS & DATA ANALYSIS, 2021, 160
[34] Unitary Similarity Preserving Linear Maps on B(H)
Karder, Mahdi
Petek, Tatjana
Taghavi, Ali
INTEGRAL EQUATIONS AND OPERATOR THEORY, 2015, 82 (01) : 51 - 60
[35] Similarity-preserving linear maps on B(H)
Ji, GX
LINEAR ALGEBRA AND ITS APPLICATIONS, 2003, 360 : 249 - 257
[36] Quasisimialarity-preserving linear maps on B(H)
Wang, Lin-Lin
Zhang, Fang-Juan
Ji, Guo-Xing
Pang, Yong-Feng
Xi'an Jianzhu Keji Daxue Xuebao/Journal of Xi'an University of Architecture and Technology, 2007, 39 (03): : 440 - 443
[37] Unitary Similarity Preserving Linear Maps on B(H)
Mahdi Karder
Tatjana Petek
Ali Taghavi
Integral Equations and Operator Theory, 2015, 82 : 51 - 60
[38] Linear maps preserving pairs of hermitian matrices on which the rank is additive and applications
Tang X.-M.
Cao C.-G.
Journal of Applied Mathematics and Computing, 2005, 19 (1-2) : 253 - 260
[39] LINEAR MAPS PRESERVING TENSOR PRODUCTS OF RANK-ONE HERMITIAN MATRICES
Xu, Jinli
Zheng, Baodong
Fosner, Ajda
JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2015, 98 (03) : 407 - 428
[40] PROPERTIES OF RANK PRESERVING WEAK MAPS
LUCAS, D
BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1974, 80 (01) : 127 - 131

← 1 2 3 4 5 →