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PreprintarXiv licencearXiv

Spectral and numerical radius preservers on pairs of unitarily similar operators

  • Zouheir Amara
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Abstract

Let ℋ be a complex Hilbert space. We characterize the bijective linear maps Φ:ℬ(ℋ)→ℬ(ℋ) that preserve the spectral radius, respectively the numerical radius, on pairs of unitarily similar operators. We also characterize bijective linear maps that transform unitary similarity into similarity. Our results cover both finite and infinite-dimensional Hilbert spaces, with no separability assumption in the latter case.

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Cite

BibTeXRIS
BibTeX
@misc{amara2026spectral,
  title = {{Spectral and numerical radius preservers on pairs of unitarily similar operators}},
  author = {Zouheir Amara},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.10635},
  eprint = {2609.10635},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.10635},
}
RIS
TY  - UNPB
TI  - Spectral and numerical radius preservers on pairs of unitarily similar operators
AU  - Zouheir Amara
PY  - 2026
DA  - 2026/09/09
PB  - arXiv
DO  - 10.48550/arxiv.2609.10635
UR  - https://arxiv.org/abs/2609.10635
AB  - Let ℋ be a complex Hilbert space. We characterize the bijective linear maps Φ:ℬ(ℋ)→ℬ(ℋ) that preserve the spectral radius, respectively the numerical radius, on pairs of unitarily similar operators. We also characterize bijective linear maps that transform unitary similarity into similarity. Our results cover both finite and infinite-dimensional Hilbert spaces, with no separability assumption in the latter case.
ER  -