Homomorphisms of $$\ell ^1$$ ℓ 1 -Munn algebras and Rees matrix semigroup algebras

Homomorphisms of $$\ell ^1$$ ℓ 1 -Munn algebras and Rees matrix semigroup algebras Let $${\mathcal {LM}}\left( {\mathcal {A}}, P\right) $$ LM A , P be an $$\ell ^1$$ ℓ 1 -Munn algebra over an arbitrary unital Banach algebra $${\mathcal {A}}$$ A . We characterize homomorphisms from $${\mathcal {LM}}\left( {\mathcal {A}}, P\right) $$ LM A , P into an arbitrary Banach algebra $${\mathcal {B}}$$ B in terms of homomorphisms from $${\mathcal {A}}$$ A into $${\mathcal {B}}$$ B . Then we discuss homomorphisms from arbitrary Banach algebras into $${\mathcal {LM}}\left( {\mathcal {A}}, P\right) $$ LM A , P . Existence and uniqueness of homomorphisms under certain conditions are also discussed. We apply these results to the concrete case of $$\ell ^1(S)$$ ℓ 1 ( S ) where S is a Rees matrix semigroup, to identify characters of $$\ell ^1(S)$$ ℓ 1 ( S ) in both cases where S is with or without zero. As a consequence if the sandwich matrix of S has a zero entry, then $$\ell ^1(S)$$ ℓ 1 ( S ) is character amenable. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Semigroup Forum Springer Journals

Homomorphisms of $$\ell ^1$$ ℓ 1 -Munn algebras and Rees matrix semigroup algebras

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Springer US
Copyright © 2016 by Springer Science+Business Media New York
Mathematics; Algebra
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