Zero product preserving maps on Banach algebras of Lipschitz functions

被引：11
|
作者：
Alaminos, J. [1 ]
Extremera, J. [1 ]
Villena, A. R. [1 ]
机构：
[1] Univ Granada, Fac Ciencias, Dept Anal Matemat, E-18071 Granada, Spain
来源：
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2010年 / 369卷 / 01期
关键词：
Algebra of Lipschitz functions; Disjointness preserving map; Map preserving zero product; Fourier algebra; Weighted Fourier algebra;
D O I：
10.1016/j.jmaa.2010.02.041
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Let (K, d) be a non-empty, compact metric space and alpha is an element of ]0, 1[. Let A be either lip(alpha)(K) or Lip(alpha)(K) and let B be a commutative unital Banach algebra. We show that every continuous linear map T : A -> B with the property that T(f)T(g) = 0 whenever f, g is an element of A are such that fg = 0 is of the form T = w Phi for some invertible element w in B and some continuous epimorphism Phi : A -> B. (C) 2010 Elsevier Inc. All rights reserved.
引用
收藏
页码：94 / 100
页数：7
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