Spaces of holomorphic functions on non-balanced domains

Abstract

This paper studies the coincidence of the T fjj and T$ topologies on the space of holomorphic functions defined on an open subset U of a Banach space. Dineen and Mujica proved that T fjj = T$ when U is a balanced open subset of a separable Banach space with the bounded approximation property. Here, we study the T W = Tg problem for several types of non-balanced domains U.

The Bloch Space on the Unit Ball of a Hilbert Space: Maximality and Multipliers

“…Then g(x) = (f (x) − λ) −1 is analytic and bounded on B H \ rB H . By Hartogs' extension type theorem from [5,Theorem 5] extend g to g analytic on B H such that g(x) = (f (x) − λ) −1 for all x ∈ B H \ rB H . Notice that if g is bounded, then Hartogs' extension g is also bounded because for the restriction g| rB H and…”