Algebras of functions with prescribed radii of boundedness and the spectra of H(u)

Abstract

We study the spectra of algebras of holomorphic functions with prescribed radii of boundedness, and use these results to study the τω and τδ spectra of H(U), where U is an open subset of a non-separable Banach space. We construct τδ continuous characters on H(U) which are not evaluations at points of U. We also discuss subsets of ℓ∞ which are bounding for H(U), U⊂ℓ∞.