Periodicity in Banach algebras

Stefan Ivkovic

Periodicity in Banach algebras

Functional Analysis 2026-06-28 v1

Authors: Stefan Ivkovic

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.

Keywords

Banach algebras periodic elements isometric isomorphism left multiplier generalized weighted shifts Hilbert modules

Cite

@article{arxiv.2606.29525,
  title  = {Periodicity in Banach algebras},
  author = {Stefan Ivkovic},
  journal= {arXiv preprint arXiv:2606.29525},
  year   = {2026}
}