CHARACTERIZING JORDAN MAPS ON C*-ALGEBRAS THROUGH ZERO PRODUCTS

被引：48
|
作者：
Alaminos, J. [1 ]
Bresar, J. M. [2 ,3 ]
Extremera, J. [1 ]
Villena, A. R. [1 ]
机构：
[1] Univ Granada, Fac Ciencias, Dept Anal Matemat, E-18071 Granada, Spain
[2] Univ Ljubljana, Fac Math & Phys, Ljubljana 1000, Slovenia
[3] Univ Maribor, Fac Nat Sci & Math, Maribor 2000, Slovenia
来源：
PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY | 2010年 / 53卷
关键词：
C*-algebra; homomorphism; Jordan homomorphism; derivation; Jordan derivation; zero-product-preserving map; DERIVATIONS; MAPPINGS; LIE;
D O I：
10.1017/S0013091509000534
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Let A and B be C*-algebras, let X be an essential Banach A-bimodule and let T : A -> B and S : A -> X be continuous linear maps with T surjective. Suppose that T(a) T(b)+ T(b) T(a) = 0 and S(a) b + bS(a) + aS(b) + S(b) a = 0 whenever a, b is an element of A are such that ab = ba = 0. We prove that then T = w Phi and S = D+Psi, where w lies in the centre of the multiplier algebra of B, Phi: A -> B is a Jordan epimorphism, D: A -> X is a derivation and Psi : A -> X is a bimodule homomorphism.
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页码：543 / 555
页数：13
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