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Homomorphisms and Composition Operators on Algebras of Analytic Functions of Bounded Type by Daniel Carando; Domingo García; Manuel Maestre is a Mathematics article available to read on EtoBox.

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Let U and V be convex and balanced open subsets of the Banach spaces X and Y, respectively. In this paper we study the following question: given two Fréchet algebras of holomorphic functions of bounded type on U and V, respectively, that are algebra isomorphic, can we deduce that X and Y (or X \* and Y \* ) are isomorphic? We prove that if X \* or Y \* has the approximation property and H wu (U ) and H wu (V ) are topologically algebra isomorphic, then X \* and Y \* are isomorphic (the converse being true when U and V are the whole space). We get analogous results for H b (U ) and H b (V ), giving conditions under which an algebra isomorphism between H b (X) and H b (Y ) is equivalent to an isomorphism between X \* and Y \* . We also obtain characterizations of different algebra homomorphisms as composition operators, study the structure of the spectrum of the algebras under consideration and show the existence of homomorphisms on H b (X) with pathological behaviors.

Who reads Homomorphisms and Composition Operators on Algebras of Analytic Functions of Bounded Type?

Author

Daniel Carando; Domingo García; Manuel Maestre

Publisher

Elsevier Science; Elsevier ; Elsevier Inc.; Elsevier BV (ISSN 0001-8708)

Published

2005

Language

EN

Field

Mathematics (Physical Sciences)