MAPS PRESERVING EQUIVALENCE BY PRODUCTS OF INVOLUTIONS

被引：2

作者：

Radic, Gordana ^{[1
,2
]}

机构：

[1] Univ Maribor, Fac Elect Engn & Comp Sci, Smetanova Ul 17, SI-2000 Maribor, Slovenia

[2] Univ Maribor, Ctr Appl Math & Theoret Phys, SI-2000 Maribor, Slovenia

来源：

OPERATORS AND MATRICES | 2019年 / 13卷 / 03期

关键词：

Linear preserver; involution; equivalence; equivalence by products of involutions; LINEAR-MAPS; SIMILARITY; SUBSPACES; OPERATORS; SPACE;

D O I：

10.7153/oam-2019-13-58

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let B(X) be the algebra of bounded linear operators on a complex Banach space X. Two operators A and B is an element of B(X) are said to be equivalent by products of involutions, if A = TBS for T and S being a products of finitely many involutions. We will give description of linear bijective maps phi on B(X) satisfying that phi (A) and phi (B) are equivalent (i.e. A = TBS for some invertible T, S is an element of B(X)) whenever A and B are equivalent by products of involutions.

引用

页码：823 / 833

页数：11

共 20 条

[1] A hereditarily indecomposable L∞-space that solves the scalar-plus-compact problem [J].

Argyros, Spiros A. ;

Haydon, Richard G. .

ACTA MATHEMATICA, 2011, 206 (01) :1-54

[2] Similarity invariant real linear subspaces and similarity preserving additive maps [J].

Du, SP ;

Hou, JC .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2004, 377 :141-153

[3]

Edelstein I.S., 1970, Funct. Anal. Appl., V4, P221

[4] SIMILARITY PRESERVING LINEAR-MAPS ON MATRICES [J].

HIAI, F .

LINEAR ALGEBRA AND ITS APPLICATIONS, 1987, 97 :127-139

[5] LINEAR-OPERATORS PRESERVING CERTAIN EQUIVALENCE-RELATIONS ON MATRICES [J].

HORN, RA ;

LI, CK ;

TSING, NK .

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 1991, 12 (02) :195-204

[6] Additive maps preserving similarity of operators on Banach spaces [J].

Hou, JC ;

Zhang, XL .

ACTA MATHEMATICA SINICA-ENGLISH SERIES, 2006, 22 (01) :179-186

[7] Similarity-invariant subspaces and similarity-preserving linear maps [J].

Ji, GX ;

Du, HK .

ACTA MATHEMATICA SINICA-ENGLISH SERIES, 2002, 18 (03) :489-498

[8] Similarity-preserving linear maps on B(H) [J].

Ji, GX .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2003, 360 :249-257

[9] Additive mappings decreasing rank one [J].

Kuzma, B .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2002, 348 (1-3) :175-187

[10] Maps preserving the nilpotency of products of operators [J].

Li, Chi-Kwong ;

Semrl, Peter ;

Sze, Nung-Sing .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2007, 424 (01) :222-239

← 1 2 →