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Norm inequalities for the spectral spread of Hermitian operators

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  • Pedro Massey
  • Demetrio Stojanoff
  • Sebastian Zarate

Abstract

In this work, we introduce a new measure for the dispersion of the spectral scale of a Hermitian (self‐adjoint) operator acting on a separable infinite‐dimensional Hilbert space that we call spectral spread. Then, we obtain some submajorization inequalities involving the spectral spread of self‐adjoint operators, that are related to Tao's inequalities for anti‐diagonal blocks of positive operators, Kittaneh's commutator inequalities for positive operators and also related to the arithmetic–geometric mean inequality. In turn, these submajorization relations imply inequalities for unitarily invariant norms (in the compact case).

Suggested Citation

  • Pedro Massey & Demetrio Stojanoff & Sebastian Zarate, 2023. "Norm inequalities for the spectral spread of Hermitian operators," Mathematische Nachrichten, Wiley Blackwell, vol. 296(9), pages 4335-4356, September.
    • Handle: RePEc:bla:mathna:v:296:y:2023:i:9:p:4335-4356
    DOI: 10.1002/mana.202200350
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