On the Lipschitz operator algebras

Ebadian, A., and Shokri, A. A.. "On the Lipschitz operator algebras." Archivum Mathematicum 045.3 (2009): 213-222. <http://eudml.org/doc/250687>.

@article{Ebadian2009,
abstract = {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 $L^\alpha _A(X,B)$.},
author = {Ebadian, A., Shokri, A. A.},
journal = {Archivum Mathematicum},
keywords = {Lipschitz algebras; amenability; homomorphism; Lipschitz algebra; amenability; homomorphism},
language = {eng},
number = {3},
pages = {213-222},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {On the Lipschitz operator algebras},
url = {http://eudml.org/doc/250687},
volume = {045},
year = {2009},
}

TY - JOUR
AU - Ebadian, A.
AU - Shokri, A. A.
TI - On the Lipschitz operator algebras
JO - Archivum Mathematicum
PY - 2009
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 045
IS - 3
SP - 213
EP - 222
AB - 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 $L^\alpha _A(X,B)$.
LA - eng
KW - Lipschitz algebras; amenability; homomorphism; Lipschitz algebra; amenability; homomorphism
UR - http://eudml.org/doc/250687
ER -