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THE FIRST COHOMOLOGY GROUP OF BANACH INVERSE SEMIGROUP ALGEBRAS WITH COEFFICIENTS IN
$L$-EMBEDDED BANACH BIMODULES
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 101 / Issue 3 / June 2020
- Published online by Cambridge University Press:
- 16 September 2019, pp. 488-495
- Print publication:
- June 2020
-
- Article
- Export citation
-
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.
