Document Type : Research Paper

Authors

Faculty of Mathematics Science and Statistics, University of Birjand, Birjand 9717851367, Birjand, Iran.

Abstract

For a discrete semigroup $S$ and a left multiplier operator  $T$ on  $S$, there is a new induced semigroup $S_{T}$, related to $S$ and $T$. In this paper, we show that if $T$ is multiplier and bijective,  then the second module cohomology groups $\mathcal{H}_{\ell^1(E)}^{2}(\ell^1(S), \ell^{\infty}(S))$ and $\mathcal{H}_{\ell^1(E_{T})}^{2}(\ell^1({S_{T}}), \ell^{\infty}(S_{T}))$ are equal, where $E$ and  $E_{T}$ are subsemigroups of idempotent elements in $S$ and $S_{T}$,   respectively.  Finally, we show thet, for every odd $n\in\mathbb{N}$,  $\mathcal{H}_{\ell^1(E_{T})}^{2}(\ell^1(S_{T}),\ell^1(S_{T})^{(n)})$ is a Banach space, when $S$ is a commutative inverse semigroup.

Keywords

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