On the Lipschitz operator algebras
Archivum mathematicum, Tome 45 (2009) no. 3, pp. 213-222
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library
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 $L^\alpha _A(X,B)$.
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 $L^\alpha _A(X,B)$.
@article{ARM_2009_45_3_a5,
author = {Ebadian, A. and Shokri, A. A.},
title = {On the {Lipschitz} operator algebras},
journal = {Archivum mathematicum},
pages = {213--222},
year = {2009},
volume = {45},
number = {3},
mrnumber = {2591677},
zbl = {1211.47074},
language = {en},
url = {http://geodesic.mathdoc.fr/item/ARM_2009_45_3_a5/}
}
Ebadian, A.; Shokri, A. A. On the Lipschitz operator algebras. Archivum mathematicum, Tome 45 (2009) no. 3, pp. 213-222. http://geodesic.mathdoc.fr/item/ARM_2009_45_3_a5/