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Clarkson--McCarthy type inequalities, part II: refinements, unitary orbits, unitarily invariant norms and ℓs--ℓs estimates

  • Teng Zhang
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Abstract

In previous work \cite{Zha26a}, the author established Clarkson--McCarthy type inequalities for several classes of operator families, including ℓp--ℓp estimates and mixed ℓq--ℓp estimates, by means of operator square-sum identities. The present paper has two main aims. First, using the tracial joint spectral measures recently introduced by O.~Heinävaara \cite{Hei25}, we obtain several refinements of the McCarthy--Clarkson inequalities, one of which confirms a conjecture of Audenaert \cite{AK17}. Second, combining tools from matrix analysis with complex interpolation theory, we establish Clarkson--McCarthy type inequalities for unitary orbits, unitarily invariant norms, and ℓs--ℓs estimates, again in the framework of operator square-sum identities.

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Cite

BibTeXRIS
BibTeX
@misc{zhang2026clarksonmccarthy,
  title = {{Clarkson--McCarthy type inequalities, part II: refinements, unitary orbits, unitarily invariant norms and $\ell_s$--$\ell_s$ estimates}},
  author = {Teng Zhang},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.00459},
  eprint = {2611.00459},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.00459},
}
RIS
TY  - UNPB
TI  - Clarkson--McCarthy type inequalities, part II: refinements, unitary orbits, unitarily invariant norms and ℓ_s--ℓ_s estimates
AU  - Teng Zhang
PY  - 2026
DA  - 2026/11/01
PB  - arXiv
DO  - 10.48550/arxiv.2611.00459
UR  - https://arxiv.org/abs/2611.00459
AB  - In previous work \cite{Zha26a}, the author established Clarkson--McCarthy type inequalities for several classes of operator families, including ℓ_p--ℓ_p estimates and mixed ℓ_q--ℓ_p estimates, by means of operator square-sum identities. The present paper has two main aims. First, using the tracial joint spectral measures recently introduced by O.~Heinävaara \cite{Hei25}, we obtain several refinements of the McCarthy--Clarkson inequalities, one of which confirms a conjecture of Audenaert \cite{AK17}. Second, combining tools from matrix analysis with complex interpolation theory, we establish Clarkson--McCarthy type inequalities for unitary orbits, unitarily invariant norms, and ℓ_s--ℓ_s estimates, again in the framework of operator square-sum identities.
ER  -