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.

Keywords

• Absolutely convex set
• Balanced set
• Boundedly regular set
• Algebra of holomorphic functions