Zero product preserving maps on Banach algebras of Lipschitz functions

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:369

Article

Alaminos, J.¹  Extremera, J.¹  Villena, A. R.¹ 

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

关键词: Algebra of Lipschitz functions;    Disjointness preserving map;    Map preserving zero product;    Fourier algebra;    Weighted Fourier algebra;   

DOI  :  10.1016/j.jmaa.2010.02.041

来源: Elsevier

【 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.

【 授权许可】

Free