Generalized notions of amenability for a class of matrix algebras

Amir Sahami

Commentationes Mathematicae Universitatis Carolinae (2019)

  • Volume: 60, Issue: 2, page 199-208
  • ISSN: 0010-2628

Abstract

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We investigate the amenability and its related homological notions for a class of I × I -upper triangular matrix algebra, say UP ( I , A ) , where A is a Banach algebra equipped with a nonzero character. We show that UP ( I , A ) is pseudo-contractible (amenable) if and only if I is singleton and A is pseudo-contractible (amenable), respectively. We also study pseudo-amenability and approximate biprojectivity of UP ( I , A ) .

How to cite

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Sahami, Amir. "Generalized notions of amenability for a class of matrix algebras." Commentationes Mathematicae Universitatis Carolinae 60.2 (2019): 199-208. <http://eudml.org/doc/294332>.

@article{Sahami2019,
abstract = {We investigate the amenability and its related homological notions for a class of $I\times I$-upper triangular matrix algebra, say $\{\rm UP\}(I,A)$, where $A$ is a Banach algebra equipped with a nonzero character. We show that $\{\rm UP\}(I,A)$ is pseudo-contractible (amenable) if and only if $I$ is singleton and $A$ is pseudo-contractible (amenable), respectively. We also study pseudo-amenability and approximate biprojectivity of $\{\rm UP\}(I,A)$.},
author = {Sahami, Amir},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {upper triangular Banach algebra; amenability; left $\varphi $-amenability; approximate biprojectivity},
language = {eng},
number = {2},
pages = {199-208},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Generalized notions of amenability for a class of matrix algebras},
url = {http://eudml.org/doc/294332},
volume = {60},
year = {2019},
}

TY - JOUR
AU - Sahami, Amir
TI - Generalized notions of amenability for a class of matrix algebras
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2019
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 60
IS - 2
SP - 199
EP - 208
AB - We investigate the amenability and its related homological notions for a class of $I\times I$-upper triangular matrix algebra, say ${\rm UP}(I,A)$, where $A$ is a Banach algebra equipped with a nonzero character. We show that ${\rm UP}(I,A)$ is pseudo-contractible (amenable) if and only if $I$ is singleton and $A$ is pseudo-contractible (amenable), respectively. We also study pseudo-amenability and approximate biprojectivity of ${\rm UP}(I,A)$.
LA - eng
KW - upper triangular Banach algebra; amenability; left $\varphi $-amenability; approximate biprojectivity
UR - http://eudml.org/doc/294332
ER -

References

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