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THE FIRST COHOMOLOGY GROUP OF BANACH INVERSE SEMIGROUP ALGEBRAS WITH COEFFICIENTS IN $L$-EMBEDDED BANACH BIMODULES

Part of: Abstract harmonic analysis Special classes of linear operators

Published online by Cambridge University Press:  16 September 2019

HOGER GHAHRAMANI Open the ORCID record for HOGER GHAHRAMANI [Opens in a new window]
HOGER GHAHRAMANI*
Affiliation:
Department of Mathematics, University of Kurdistan, P. O. Box 416, Sanandaj, Iran email [email protected], [email protected]
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Abstract

Let $S$ be a discrete inverse semigroup, $l^{1}(S)$ the Banach semigroup algebra on $S$ and $\mathbb{X}$ a Banach $l^{1}(S)$-bimodule which is an $L$-embedded Banach space. We show that under some mild conditions ${\mathcal{H}}^{1}(l^{1}(S),\mathbb{X})=0$. We also provide an application of the main result.

Keywords

Banach inverse semigroup algebrafirst cohomology groupderivation

MSC classification

Primary: 43A20: $L^1$-algebras on groups, semigroups, etc.
Secondary: 47B47: Commutators, derivations, elementary operators, etc.
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 101 , Issue 3 , June 2020 , pp. 488 - 495
Copyright
© 2019 Australian Mathematical Publishing Association Inc.

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