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

页码：94 / 100

页数：7

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