# 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

, Volume 95 (1) – Feb 16, 2016
12 pages

/lp/springer_journal/homomorphisms-of-ell-1-1-munn-algebras-and-rees-matrix-semigroup-TcKVEp9UGv
Publisher
Springer US
Subject
Mathematics; Algebra
ISSN
0037-1912
eISSN
1432-2137
D.O.I.
10.1007/s00233-016-9774-0
Publisher site
See Article on Publisher Site

### Abstract

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.

### Journal

Semigroup ForumSpringer Journals

Published: Feb 16, 2016

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