Homomorphisms between Algebras of Holomorphic Functions

Abstract EN

For two complex Banach spaces X and Y , in this paper, we study the generalized spectrum ℳ b ( X , Y ) of all nonzero algebra homomorphisms from ℋ b ( X ) , the algebra of all bounded type entire functions on X , into ℋ b ( Y ) .

We endow ℳ b ( X , Y ) with a structure of Riemann domain over ℒ ( 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 ℳ b , ∞ ( X , B Y ) of all nonzero algebra homomorphisms from ℋ b ( X ) into ℋ ∞ ( B Y ) of bounded holomorphic functions on the open unit ball of Y and ℳ ∞ ( B X , B Y ) of all nonzero algebra homomorphisms from ℋ ∞ ( B X ) into ℋ ∞ ( B Y ) .