On approximation of homomorphisms of algebras of entire functions on Banach spaces

Keywords:
analytic functions on Banach space, homomorphisms of algebras of analytic functions, approximation property
Published online:
2019-06-30
Abstract
It is known due to R. Aron, B. Cole and T. Gamelin that every complex homomorphism of the algebra of entire functions of bounded type on a Banach space X can be approximated in some sense by a net of point valued homomorphism. In this paper we consider the question about a generalization of this result for the case of homomorphisms to any commutative Banach algebra A. We obtained some positive results if A is the algebra of uniformly continuous analytic functions on the unit ball of X.
How to Cite
(1)
Pryimak, H. On Approximation of Homomorphisms of Algebras of Entire Functions on Banach Spaces. Carpathian Math. Publ. 2019, 11, 158-162.