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Davood Alimohammadi

Davood Alimohammadi

Academic rank: Associate Professor
ORCID: https://orcid.org/0000-0002-9398-6213
Education: PhD.
ScopusId: 6505995626
HIndex:
Faculty: Science
Address: Arak University
Phone:

Research

Title
Ideales, point derivations, amenability and weak amenability of extended Lipschitz algebras
Type
Presentation
Keywords
Amenability, Banach function algebra, Extended Lipschitz algebra, Point derivation, Weak amenability
Year
2016
Researchers Davood Alimohammadi ، MALIHEH MAYGHANI

Abstract

Let $(X,d)$ be a compact metric space and let $K$ be a nonempty compact subset of $X.$ Let $\alpha \in (0, 1]$ and let ${\rm Lip}(X,K,d^\alpha)$ denote the algebra of all $f \in C(X)$ for which $f|_{K} \in {\rm Lip(K, d^{\alpha})}$. In this paper we first study the structure of certain ideals of the algebra ${\rm Lip}(X,K,d^\alpha)$. Next we show that if $K$ is infinite and ${\rm int}(K)$ contains a limit point of $K$ then ${\rm Lip}(X,K,d^\alpha)$ has at least a nonzero continuous point derivation and applying this fact we prove that ${\rm Lip}(X,K,d^\alpha)$ is not weakly amenable and amenable.