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Title: On the Lipschitz operator algebras (English)
Author: Ebadian, A.
Author: Shokri, A. A.
Language: English
Journal: Archivum Mathematicum
ISSN: 0044-8753 (print)
ISSN: 1212-5059 (online)
Volume: 45
Issue: 3
Year: 2009
Pages: 213-222
Summary lang: English
Category: math
Summary: In a recent paper by H. X. Cao, J. H. Zhang and Z. B. Xu an $\alpha $-Lipschitz operator from a compact metric space into a Banach space $A$ is defined and characterized in a natural way in the sence that $F:K\rightarrow A$ is a $\alpha $-Lipschitz operator if and only if for each $\sigma \in X^*$ the mapping $\sigma \circ F$ is a $\alpha $-Lipschitz function. The Lipschitz operators algebras $L^\alpha (K,A)$ and $l^\alpha (K,A)$ are developed here further, and we study their amenability and weak amenability of these algebras. Moreover, we prove an interesting result that $L^\alpha (K,A)$ and $l^\alpha (K,A)$ are isometrically isomorphic to $L^{\alpha }(K)\check{\otimes }A$ and $l^{\alpha }(K)\check{\otimes }A$ respectively. Also we study homomorphisms on the $L^\alpha _A(X,B)$. (English)
Keyword: Lipschitz algebras
Keyword: amenability
Keyword: homomorphism
MSC: 46H25
MSC: 46J10
MSC: 47B48
idZBL: Zbl 1211.47074
idMR: MR2591677
Date available: 2009-09-18T11:25:08Z
Last updated: 2013-09-19
Stable URL:
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