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, and show that the algebra of holomorphic functions on a compact set is such an 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 algebras, and in particular, in the associated Wiener algebra.
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D. Alpay thanks the Earl Katz family for endowing the chair which supported his research, and the Binational Science Foundation Grant No. 2010117.
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Alpay, D., Salomon, G. On Algebras Which are Inductive Limits of Banach Spaces. Integr. Equ. Oper. Theory 83, 211–229 (2015). https://doi.org/10.1007/s00020-015-2220-y
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DOI: https://doi.org/10.1007/s00020-015-2220-y