On algebras which are inductive limits of Banach spaces

2013/02/14 by Daniel Alpay, Guy Salomon, Alpay, Daniel +1
Mathematics · #43A15. Secondary: 13J99 #60H40 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #Primary: 16S99 #math.FA #msc:13J99 #msc:16S99 #msc:43A15. #msc:60H40

paper · pdf · doi:10.48550/arxiv.1302.3372

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openalex publication_date 2013/02/14 · arxiv created 2013/04/28 · arxiv updated 2013/04/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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