Eigenvalue inequalities for differences of means of Hilbert space operators

We prove several eigenvalue inequalities for the differences of various means of two positive invertible operators A and B on a separable Hilbert space, under the assumption that A-B is compact. Equality conditions of these inequalities are also obtained.

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Bibliographic Details
Published in:Linear algebra and its applications 2012-03, Vol.436 (5), p.1516-1527
Main Authors: Hirzallah, Omar, Kittaneh, Fuad, Krnić, Mario, Lovričević, Neda, Pečarić, Josip
Format: Article
Language:English
Subjects:
Algebra
Arithmetic operator mean
Compact operator
Eigenvalue
Exact sciences and technology
Geometric operator mean
Heinz operator mean
Inequality
Linear and multilinear algebra, matrix theory
Mathematical analysis
Mathematics
Operator theory
Positive operator
Sciences and techniques of general use
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Description
Summary:We prove several eigenvalue inequalities for the differences of various means of two positive invertible operators A and B on a separable Hilbert space, under the assumption that A-B is compact. Equality conditions of these inequalities are also obtained.
ISSN:0024-3795
1873-1856
DOI:10.1016/j.laa.2011.08.037