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THE FIRST COHOMOLOGY GROUP OF BANACH INVERSE SEMIGROUP ALGEBRAS WITH COEFFICIENTS IN $L$-EMBEDDED BANACH BIMODULES
Published online by Cambridge University Press: 16 September 2019
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.
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- © 2019 Australian Mathematical Publishing Association Inc.
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