New classes of spaceable sets of analytic functions on the open unit disk

TL;DR

This paper explores the algebraic and topological structures of certain classes of analytic functions on the open unit disk, focusing on unbounded Bloch functions and bounded type functions within a Banach algebra, highlighting their spaceability properties.

Contribution

It introduces new classes of spaceable sets of analytic functions on the open unit disk, expanding understanding of their algebraic and topological structures.

Findings

Identification of spaceable sets within classes of Bloch functions

Analysis of algebraic structures in bounded type functions

Demonstration of topological properties of these function classes

Abstract

In this paper we study an algebraic and topological structure inside the following sets of special functions: Bloch functions defined on the open unit disk that are unbounded and analytic functions of bounded type defined a Banach algebra E into E, which are not Lorch-analytic.