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For extending the notion of -algebra, as defined in [2], we present an example of an m-admissible algebra which is not an - algebra. Then we define -subcompactification and -subcompactification to study the universal -subcompactification and the universal -subcompactification from the function algebras point of view.
Character inner amenability for a certain class of Banach algebras including projective tensor products, Lau products and module extensions is investigated. Some illuminating examples are given.
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