Linear preservers of equivalence relations on infinite-dimensional spaces

被引：8

作者：

Petek, Tatjana ^{[1
,2
]}

Radic, Gordana ^{[1
]}

机构：

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

[2] Inst Math Phys & Mech, Jadranska Ul 19, SI-1000 Ljubljana, Slovenia

来源：

STUDIA MATHEMATICA | 2017年 / 238卷 / 02期

关键词：

linear preservers; equivalence preservers; preservers of equivalence by unitaries; congruence preservers; ADDITIVE MAPS; SIMILARITY; OPERATORS; MATRICES; MAPPINGS; B(H); INVERTIBILITY;

D O I：

10.4064/sm8356-12-2016

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Linear maps preserving equivalence, equivalence by unitaries or congruence, acting on an infinite-dimensional Banach/Hilbert space, are classified. In the first two cases a unified approach is used: we identify the orbit of the identity and show that it is invariant under the map under consideration. Known results on linear invertibility or unitary group preservers are then used.

引用

页码：101 / 119

页数：19

共 24 条

[1]

[Anonymous], 2013, Matrix Analysis

[2]

Bresar M., 1997, Banach Center Publications, V38, P49

[3] Nonlinear maps preserving similarity on B(H) [J].

Du, Shuanping ;

Hou, Jinchuan ;

Bai, Zhaofang .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2007, 422 (2-3) :506-516

[4] Additive maps preserving similarity or asymptotic similarity on B(H) [J].

Du, Shuanping ;

Hou, Jinchuan ;

Bai, Zhaofang .

LINEAR & MULTILINEAR ALGEBRA, 2007, 55 (03) :209-218

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

Du, SP ;

Hou, JC .

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

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

HIAI, F .

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

[7] 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

[8] Congruences of a square matrix and its transpose [J].

Horn, RA ;

Sergeichuk, VV .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2004, 389 :347-353

[9] Canonical forms for complex matrix congruence and *congruence [J].

Horn, Rodger A. ;

Sergeichuk, Vladimir V. .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2006, 416 (2-3) :1010-1032

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

Hou, JC ;

Zhang, XL .

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

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