On bilinear maps determined by rank one idempotents

被引：13

作者：

Alaminos, J. ^{[3
]}

Bresar, M. ^{[1
,2
]}

Extremera, J. ^{[3
]}

Villena, A. R. ^{[3
]}

机构：

[1] Univ Ljubljana, Fac Math & Phys, Ljubljana 61000, Slovenia

[2] Univ Maribor, Fac Nat Sci & Math, Maribor, Slovenia

[3] Univ Granada, Fac Ciencias, Dept Anal Matemat, E-18071 Granada, Spain

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2010年 / 432卷 / 2-3期

关键词：

Matrix algebra; Zero product; Rank one idempotent; Linear map; Bilinear map; Linear preserver problem; DERIVATIONS; ALGEBRAS;

D O I：

10.1016/j.laa.2009.09.017

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let M-n, n >= 2, be the algebra of all n x n matrices over a field F of characteristic not 2, and let Phi be a bilinear map from M-n x M-n into an arbitrary vector space X over F. Our main result states that if phi (e, f) = 0 whenever e and f are orthogonal rank one idempotents, then there exist linear maps Phi(1), Phi(2) : Mn -> X such that phi (a, b) = Phi(1) (ab) + Phi(2) (ba) for all a, b is an element of M-n. This is applicable to some linear preserver problems. (C) 2009 Elsevier Inc. All rights reserved.

引用

页码：738 / 743

页数：6

共 8 条

[1]

Alaminos J, 2007, P ROY SOC EDINB A, V137, P1

[2] Maps preserving zero products [J].

Alaminos, J. ;

Bresar, M. ;

Extremera, J. ;

Villena, A. R. .

STUDIA MATHEMATICA, 2009, 193 (02) :131-159

[3]

ALAMINOS J, P EDINBURGH IN PRESS

[4] On bilinear maps on matrices with applications to commutativity preservers [J].

Bresar, M ;

Semrl, P .

JOURNAL OF ALGEBRA, 2006, 301 (02) :803-837

[5] MAPPINGS WHICH PRESERVE IDEMPOTENTS, LOCAL AUTOMORPHISMS, AND LOCAL DERIVATIONS [J].

BRESAR, M ;

SEMRL, P .

CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 1993, 45 (03) :483-496

[6] Zero product determined matrix algebras [J].

Bresar, Matej ;

Grasic, Mateja ;

Sanchez Ortega, Juana .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2009, 430 (5-6) :1486-1498

[7]

GRASIC M, LINEAR MULT IN PRESS

[8]

Molnar L., 2007, LECT NOTES MATH

← 1 →