Abstract
For an arbitrary normed algebra with an approximate identity, we introduce some notions of invertibility of a net in this algebra with respect to the given approximate identity. By means of that, we show a Wiener-Tauberian type theorem in that general situation. An application yields an abstract Wiener-Tauberian theorem for a class of commutative Banach algebras, which implies the classical Wiener-Tauberian theorem for locally compact Abelian groups.
Citation
Tobias BLENDEK. "A Wiener-Tauberian Type Theorem for Arbitrary Normed Algebras with an Approximate Identity." Tokyo J. Math. 37 (1) 179 - 184, June 2014. https://doi.org/10.3836/tjm/1406552437
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