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Some Exponential Inequalities for Semisimple Lie Groups

  • Tin-Yau Tam
Conference paper
Part of the Operator Theory: Advances and Applications book series (OT, volume 202)

Abstract

Let ∥ · ∥ be any give unitarily invariant norm. We obtain some exponential relations in the context of semisimple Lie group. On one hand they extend the inequalities (1) ∥e A ∥ ≤ ∥e Re A∥ for all A ∈ ∝ n ×n where Re A denotes the Hermitian part of A, and (2) ∥e A+B ∥ ≤ ∥e A e B ∥, where A and B are n×n Hermitian matrices. On the other hand, the inequalities of Weyl, Ky Fan, Golden-Thompson, Lenard-Thompson, Cohen, and So-Thompson are recovered. Araki’s relation on (e A/2 e R e A/2) r and e rA/2 e rB e rA/2, where A,B are Hermitian and ∈ ℝ, is extended.

Keywords

Singular values eigenvalue moduli spectral radius pre-order 

Mathematics Subject Classification (2000)

Primary 15A45 22E46 Secondary 15A42 

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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2010

Authors and Affiliations

  • Tin-Yau Tam
    • 1
  1. 1.Department of Mathematics and StatisticsAuburn UniversityUSA

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