Approximate amenability of certain inverse semigroup algebras |
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Authors: | Mehdi ROSTAMI Abdolrasoul POURABBAS Morteza ESSMAILI |
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Institution: | 1. Faculty of Mathematical and Computer Science, Amirkabir University of Technology, 424 Hafez Avenue, 15914 Tehran, Iran;2. Faculty of Mathematical and Computer Science, Kharazmi University, 50 Taleghani Avenue, 15618 Tehran, Iran |
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Abstract: | In this article, the approximate amenability of semigroup algebra ?1(S) is investigated, where (S) is a uniformly locally finite inverse semigroup. Indeed, we show that for a uniformly locally finite inverse semigroup (S), the notions of amenability, approximate amenability and bounded approximate amenability of ?1(S) are equivalent. We use this to give a direct proof of the approximate amenability of ?1(S) for a Brandt semigroup (S). Moreover, we characterize the approximate amenability of ?1(S), where S is a uniformly locally finite band semigroup. |
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Keywords: | Approximate amenability semigroup algebras uniformly locally finite inverse semigroup Brandt semigroup |
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