Abstract: The study of different notions of amenability on a given category of objects, have been one of the most fundamental areas of research in abstract harmonic analysis. In this talk, we first provide a preliminary overview of the category of semihypergroups. As the name itself suggests, the category of semihypergroups can be regarded simply as a natural extension to the category of locally compact semigroups, with abundant examples in different areas of research. We then introduce the concept of amenability in this broader setting, and discuss several characterizations of the same in terms of certain ergodic, stationary, Banach algebraic and hereditary properties of the associated convolutive measure algebras.
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