Some Exponential Inequalities for Semisimple Lie Groups View Full Text


Ontology type: schema:Chapter     


Chapter Info

DATE

2010

AUTHORS

Joseph A. Ball , Vladimir Bolotnikov , Leiba Rodman , J. William Helton , Ilya M. Spitkovsky , Tin-Yau Tam

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. More... »

PAGES

539-552

References to SciGraph publications

Book

TITLE

Topics in Operator Theory

ISBN

978-3-0346-0157-3
978-3-0346-0158-0

Author Affiliations

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/978-3-0346-0158-0_32

DOI

http://dx.doi.org/10.1007/978-3-0346-0158-0_32

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1008812953


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