Abstract and Applied Analysis

Homomorphisms between Algebras of Holomorphic Functions

Verónica Dimant, Domingo García, Manuel Maestre, and Pablo Sevilla-Peris

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Abstract

For two complex Banach spaces X and Y , in this paper, we study the generalized spectrum b ( X , Y ) of all nonzero algebra homomorphisms from b ( X ) , the algebra of all bounded type entire functions on X , into b ( Y ) . We endow b ( X , Y ) with a structure of Riemann domain over ( X * , Y * ) whenever X is symmetrically regular. The size of the fibers is also studied. Following the philosophy of (Aron et al., 1991), this is a step to study the set b , ( X , B Y ) of all nonzero algebra homomorphisms from b ( X ) into ( B Y ) of bounded holomorphic functions on the open unit ball of Y and ( B X , B Y ) of all nonzero algebra homomorphisms from ( B X ) into ( B Y ) .

Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2014), Article ID 612304, 12 pages.

Dates
First available in Project Euclid: 2 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1412278777

Digital Object Identifier
doi:10.1155/2014/612304

Mathematical Reviews number (MathSciNet)
MR3212436

Zentralblatt MATH identifier
07022722

Citation

Dimant, Verónica; García, Domingo; Maestre, Manuel; Sevilla-Peris, Pablo. Homomorphisms between Algebras of Holomorphic Functions. Abstr. Appl. Anal. 2014, Special Issue (2014), Article ID 612304, 12 pages. doi:10.1155/2014/612304. https://projecteuclid.org/euclid.aaa/1412278777


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