Entire Analytic Functions of Unbounded Type on Banach Spaces and Their Lineability

• Main Authors: Andriy Zagorodnyuk, Anna Hihliuk
• Format: Article
• Language: English
• Published: MDPI AG 2021-07-01
• Series: Axioms
• Subjects: analytic functions on Banach spaces; functions of unbounded type; symmetric polynomials on Banach spaces
• Online Access: https://www.mdpi.com/2075-1680/10/3/150

In the paper we establish some conditions under which a given sequence of polynomials on a Banach space <i>X</i> supports entire functions of unbounded type, and construct some counter examples. We show that if <i>X</i> is an infinite dimensional Banach space, then the set of entire functions of unbounded type can be represented as a union of infinite dimensional linear subspaces (without the origin). Moreover, we show that for some cases, the set of entire functions of unbounded type generated by a given sequence of polynomials contains an infinite dimensional algebra (without the origin). Some applications for symmetric analytic functions on Banach spaces are obtained.