Some algebraic and homological properties of Lipschitz algebras and their second duals

F. Abtahi; E. Byabani; A. Rejali

Archivum Mathematicum (2019)

  • Volume: 055, Issue: 4, page 211-224
  • ISSN: 0044-8753

Abstract

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Let ( X , d ) be a metric space and α > 0 . We study homological properties and different types of amenability of Lipschitz algebras Lip α X and their second duals. Precisely, we first provide some basic properties of Lipschitz algebras, which are important for metric geometry to know how metric properties are reflected in simple properties of Lipschitz functions. Then we show that all of these properties are equivalent to either uniform discreteness or finiteness of X . Finally, some results concerning the character space and Arens regularity of Lipschitz algebras are provided.

How to cite

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Abtahi, F., Byabani, E., and Rejali, A.. "Some algebraic and homological properties of Lipschitz algebras and their second duals." Archivum Mathematicum 055.4 (2019): 211-224. <http://eudml.org/doc/294220>.

@article{Abtahi2019,
abstract = {Let $(X,d)$ be a metric space and $\alpha >0$. We study homological properties and different types of amenability of Lipschitz algebras $\operatorname\{Lip\}_\alpha X$ and their second duals. Precisely, we first provide some basic properties of Lipschitz algebras, which are important for metric geometry to know how metric properties are reflected in simple properties of Lipschitz functions. Then we show that all of these properties are equivalent to either uniform discreteness or finiteness of $X$. Finally, some results concerning the character space and Arens regularity of Lipschitz algebras are provided.},
author = {Abtahi, F., Byabani, E., Rejali, A.},
journal = {Archivum Mathematicum},
keywords = {amenability; Arens regularity; biprojectivity; biflatness; Lipschitz algebra; metric space},
language = {eng},
number = {4},
pages = {211-224},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Some algebraic and homological properties of Lipschitz algebras and their second duals},
url = {http://eudml.org/doc/294220},
volume = {055},
year = {2019},
}

TY - JOUR
AU - Abtahi, F.
AU - Byabani, E.
AU - Rejali, A.
TI - Some algebraic and homological properties of Lipschitz algebras and their second duals
JO - Archivum Mathematicum
PY - 2019
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 055
IS - 4
SP - 211
EP - 224
AB - Let $(X,d)$ be a metric space and $\alpha >0$. We study homological properties and different types of amenability of Lipschitz algebras $\operatorname{Lip}_\alpha X$ and their second duals. Precisely, we first provide some basic properties of Lipschitz algebras, which are important for metric geometry to know how metric properties are reflected in simple properties of Lipschitz functions. Then we show that all of these properties are equivalent to either uniform discreteness or finiteness of $X$. Finally, some results concerning the character space and Arens regularity of Lipschitz algebras are provided.
LA - eng
KW - amenability; Arens regularity; biprojectivity; biflatness; Lipschitz algebra; metric space
UR - http://eudml.org/doc/294220
ER -

References

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