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Trace inequalities for logarithms and powers of [formula omitted]-Hermitian matrices

Authors
Journal
Linear Algebra and its Applications
0024-3795
Publisher
Elsevier
Publication Date
Volume
432
Issue
12
Identifiers
DOI: 10.1016/j.laa.2010.01.017
Keywords
  • Indefinite Inner Product Space
  • [Formula Omitted]-Hermitian Matrix
  • Relative Entropy
  • Tsallis Entropy
  • Klein Inequality
  • Peierls–Bogoliubov Inequality
Disciplines
  • Mathematics

Abstract

Abstract Spectral inequalities are stated for the trace of the exponential or the logarithmic of certain J -Hermitian matrices, J = I r ⊕ - I n - r , 0 < r < n . The obtained inequalities are established in the context of indefinite inner product spaces, and they are known to be valid for Hilbert space operators or operator algebras.

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