Approximate biflatness and Johnson pseudo-contractibility of some Banach algebras

Amir Sahami; Mohammad R. Omidi; Eghbal Ghaderi; Hamzeh Zangeneh

Commentationes Mathematicae Universitatis Carolinae (2020)

  • Volume: 61, Issue: 1, page 83-92
  • ISSN: 0010-2628

Abstract

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We study the structure of Lipschitz algebras under the notions of approximate biflatness and Johnson pseudo-contractibility. We show that for a compact metric space X , the Lipschitz algebras Lip α ( X ) and lip α ( X ) are approximately biflat if and only if X is finite, provided that 0 < α < 1 . We give a necessary and sufficient condition that a vector-valued Lipschitz algebras is Johnson pseudo-contractible. We also show that some triangular Banach algebras are not approximately biflat.

How to cite

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Sahami, Amir, et al. "Approximate biflatness and Johnson pseudo-contractibility of some Banach algebras." Commentationes Mathematicae Universitatis Carolinae 61.1 (2020): 83-92. <http://eudml.org/doc/296984>.

@article{Sahami2020,
abstract = {We study the structure of Lipschitz algebras under the notions of approximate biflatness and Johnson pseudo-contractibility. We show that for a compact metric space $X$, the Lipschitz algebras $\{\rm Lip\}_\{\alpha \}(X)$ and $\{\rm lip\}_\{\alpha \}(X)$ are approximately biflat if and only if $X$ is finite, provided that $0<\alpha <1$. We give a necessary and sufficient condition that a vector-valued Lipschitz algebras is Johnson pseudo-contractible. We also show that some triangular Banach algebras are not approximately biflat.},
author = {Sahami, Amir, Omidi, Mohammad R., Ghaderi, Eghbal, Zangeneh, Hamzeh},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {approximate biflatness; Johnson pseudo-contractibility; Lipschitz algebra; triangular Banach algebra},
language = {eng},
number = {1},
pages = {83-92},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Approximate biflatness and Johnson pseudo-contractibility of some Banach algebras},
url = {http://eudml.org/doc/296984},
volume = {61},
year = {2020},
}

TY - JOUR
AU - Sahami, Amir
AU - Omidi, Mohammad R.
AU - Ghaderi, Eghbal
AU - Zangeneh, Hamzeh
TI - Approximate biflatness and Johnson pseudo-contractibility of some Banach algebras
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2020
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 61
IS - 1
SP - 83
EP - 92
AB - We study the structure of Lipschitz algebras under the notions of approximate biflatness and Johnson pseudo-contractibility. We show that for a compact metric space $X$, the Lipschitz algebras ${\rm Lip}_{\alpha }(X)$ and ${\rm lip}_{\alpha }(X)$ are approximately biflat if and only if $X$ is finite, provided that $0<\alpha <1$. We give a necessary and sufficient condition that a vector-valued Lipschitz algebras is Johnson pseudo-contractible. We also show that some triangular Banach algebras are not approximately biflat.
LA - eng
KW - approximate biflatness; Johnson pseudo-contractibility; Lipschitz algebra; triangular Banach algebra
UR - http://eudml.org/doc/296984
ER -

References

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