On algebras which are inductive limits of Banach spaces
Daniel Alpay, Guy Salomon

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.
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Taxonomy
TopicsMathematical Analysis and Transform Methods · Advanced Operator Algebra Research · Advanced Topics in Algebra
