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arXiv · 2606.29525

Periodicity in Banach algebras

Stefan Ivkovic
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Abstract

In this paper, we consider operators that are compositions of an isometric isomorphism and a left multiplier on a Banach algebra, and we provide necessary and sufficient conditions for these operators to have a dense set of periodic elements. As an application of this result, we characterize generalized weighted shifts with a dense set of periodic elements on the standard Hilbert module over C*-algebra of compact operators on a separable Hilbert space. As another application, we characterize generalized weighted shifts with a dense set of periodic elements on the standard Hilbert module over commutative non-unital C*-algebra.

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Stefan Ivkovic. 2026-06-28. Periodicity in Banach algebras. https://arxiv.org/abs/2606.29525

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