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Abstract and Applied Analysis
Volume 2014, Article ID 612304, 12 pages
http://dx.doi.org/10.1155/2014/612304
Research Article

Homomorphisms between Algebras of Holomorphic Functions

1Departamento de Matemática, Universidad de San Andrés, Vito Dumas 284, Victoria, B1644BID Buenos Aires, Argentina
2Departamento de Análisis Matemático, Universidad de Valencia, Doctor Moliner 50, Burjasot, 46100 Valencia, Spain
3Instituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, 46022 Valencia, Spain

Received 26 December 2013; Accepted 13 March 2014; Published 12 May 2014

Academic Editor: Alfredo Peris

Copyright © 2014 Verónica Dimant et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

For two complex Banach spaces and , in this paper, we study the generalized spectrum of all nonzero algebra homomorphisms from , the algebra of all bounded type entire functions on , into . We endow with a structure of Riemann domain over whenever 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 of all nonzero algebra homomorphisms from into of bounded holomorphic functions on the open unit ball of and of all nonzero algebra homomorphisms from into .