# On the Lipschitz operator algebras

Archivum Mathematicum (2009)

- Volume: 045, Issue: 3, page 213-222
- ISSN: 0044-8753

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topEbadian, 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 -

## References

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