Envelopes of open sets and extending holomorphic functions on dual Banach spaces

Abstract

We investigate certain envelopes of open sets in dual Banach spaces which are related to extending holomorphic functions. We give a variety of examples of absolutely convex sets showing that the extension is in many cases not possible. We also establish connections to the study of iterated weak* sequential closures of convex sets in the dual of separable spaces.

20 pages

References in corpus (2)

• Spectra of weighted algebras of holomorphic functions
• W^*-derived sets of transfinite order of subspaces of dual Banach spaces

Cited by in corpus (1)

• Weak${}^{\ast }$ derived sets of convex sets in duals of non-reflexive spaces