Homomorphisms between Algebras of Holomorphic Functions

Abstract

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