The behavior of iterates of multipliers in commutative Banach algebras

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Mustafayev H., Topal H.

ANNALES POLONICI MATHEMATICI, vol.128, pp.233-247, 2022 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 128
  • Publication Date: 2022
  • Doi Number: 10.4064/ap210627-2-12
  • Journal Name: ANNALES POLONICI MATHEMATICI
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
  • Page Numbers: pp.233-247
  • Keywords: commutative Banach algebra, multiplier, locally compact abelian group, group algebra, measure algebra, convergence, KATZNELSON-TZAFRIRI TYPE, THEOREMS
  • Van Yüzüncü Yıl University Affiliated: Yes

Abstract

Let A be a complex, commutative, and semisimple Banach algebra and let T be a power bounded multiplier on A. We prove a Katznelson-Tzafriri type theorem for T. As an application, we give some results concerning convergence of the sequence {T(n)a} (a is an element of A). Some related problems are also discussed.