Geodesic
Some algebraic and homological properties of Lipschitz algebras and their second duals
Archivum mathematicum, Tome 55 (2019) no. 4, pp. 211-224.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

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.
DOI : 10.5817/AM2019-4-211
Classification : 11J83, 46H05, 46J10
Keywords: amenability; Arens regularity; biprojectivity; biflatness; Lipschitz algebra; metric space 
@article{10_5817_AM2019_4_211,
     author = {Abtahi, F. and Byabani, E. and Rejali, A.},
     title = {Some algebraic and homological properties of {Lipschitz} algebras and their second duals},
     journal = {Archivum mathematicum},
     pages = {211--224},
     publisher = {mathdoc},
     volume = {55},
     number = {4},
     year = {2019},
     doi = {10.5817/AM2019-4-211},
     mrnumber = {40383556},
     zbl = {07144736},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.5817/AM2019-4-211/}
}
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
SP  - 211
EP  - 224
VL  - 55
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.5817/AM2019-4-211/
DO  - 10.5817/AM2019-4-211
LA  - en
ID  - 10_5817_AM2019_4_211
ER  - 
%0 Journal Article
%A Abtahi, F.
%A Byabani, E.
%A Rejali, A.
%T Some algebraic and homological properties of Lipschitz algebras and their second duals
%J Archivum mathematicum
%D 2019
%P 211-224
%V 55
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.5817/AM2019-4-211/
%R 10.5817/AM2019-4-211
%G en
%F 10_5817_AM2019_4_211
Abtahi, F.; Byabani, E.; Rejali, A. Some algebraic and homological properties of Lipschitz algebras and their second duals. Archivum mathematicum, Tome 55 (2019) no. 4, pp. 211-224. doi : 10.5817/AM2019-4-211. http://geodesic.mathdoc.fr/articles/10.5817/AM2019-4-211/

Cité par Sources :