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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. Finally, in the last section of the paper, we provide extensions of these results from the case of a sequence generated by powers of a single operator to families of operators indexed over a countable set.

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Cite

BibTeXRIS
BibTeX
@misc{ivkovic2026periodicity,
  title = {{Periodicity in Banach algebras}},
  author = {Stefan Ivkovic},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2606.29525},
  eprint = {2606.29525},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2606.29525},
}
RIS
TY  - UNPB
TI  - Periodicity in Banach algebras
AU  - Stefan Ivkovic
PY  - 2026
DA  - 2026/10/30
PB  - arXiv
DO  - 10.48550/arxiv.2606.29525
UR  - https://arxiv.org/abs/2606.29525
AB  - 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. Finally, in the last section of the paper, we provide extensions of these results from the case of a sequence generated by powers of a single operator to families of operators indexed over a countable set.
ER  -