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- Title
Unital Compact Homomorphisms between Extended Analytic Lipschitz Algebras.
- Authors
Alimohammadi, Davood; Mayghani, Maliheh
- Abstract
Let X and K be compact plane sets with K C̱ X. We define A(X,K) = {f ∈ C(X) : f|K ∈ A(K)}, where A(K) = {g ∈ C(X) : g is analytic on int(K)}. For α ∈ (0, 1}, we define Lip(X,K,α) = {f ∈ C(X): pα,K(f) = sup{|f(z) - f(w)|/|z - w|α : z,w ∈ K, z ≠ w} < ∞} and LipA(X,K,α) = A(X,K) ∩ Lip(X,K,α). It is known that LipA(X,K,α) is a natural Banach function algebra on X under the norm ||f||Lip(X,K,α) = ||f||X + pα,K(f), where ||f||X = sup{|f(x)| : x ∈ X}. These algebras are called extended analytic Lipschitz algebras. In this paper we study unital homomorphisms from natural Banach function subalgebras of LipA(X1,K1, α1) to natural Banach function subalgebras of LipA(X2,K2,α2) and investigate necessary and sufficient conditions for which these homomorphisms are compact. We also determine the spectrum of unital compact endomorphisms of LipA(X,K,α).
- Subjects
HOMOMORPHISMS; LIPSCHITZ spaces; SET theory; IDEAL spaces (Mathematics); ENDOMORPHISMS; FUNCTION spaces; GROUP theory
- Publication
Abstract & Applied Analysis, 2011, p1
- ISSN
1085-3375
- Publication type
Article
- DOI
10.1155/2011/146758