On algebras which are inductive limits of Banach spaces

TL;DR

This paper introduces a new class of algebras formed as inductive limits of Banach spaces, establishes a Wiener theorem for these algebras, and explores their factorization properties.

Contribution

It defines inductive limit Banach algebras with norm inequalities, constructs an associated Wiener algebra, and proves a Wiener theorem within this framework.

Findings

Established inequalities analogous to Banach algebra norms

Proved a Wiener theorem for the new algebra class

Analyzed factorization properties in these algebras

Abstract

We introduce algebras which are inductive limits of Banach spaces and carry inequalities which are counterparts of the inequality for the norm in a Banach algebra. We then define an associated Wiener algebra, and prove the corresponding version of the well-known Wiener theorem. Finally, we consider factorization theory in these algebra, and in particular, in the associated Wiener algebra.