On the Singular Values of a Product of Operators

Previous article Next article On the Singular Values of a Product of OperatorsRajendra Bhatia and Fuad KittanehRajendra Bhatia and Fuad Kittanehhttps: //doi. org/10. 1137/0611018PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAboutAbstractFor compact Hilbert space operators A and B, the singular values of A^ * B are shown to be dominated by those of 12 (AA^* + BB^*). 1 Rajendra Bhatia, Perturbation inequalities for the absolute value map in norm ideals of operators, J. Operator Theory, 19 (1988), 129–136 89g: 47010 0698. 47029 ISIGoogle Scholar2 C. K. Fong, Norm estimates related to self-commutators, Linear Algebra Appl. , 74 (1986), 151–156 10. 1016/0024-3795 (86) 90118-7 87c: 15047 0588. 15009 CrossrefISIGoogle Scholar3 I. C. Gohberg and, M. G. Krei˘ n, Introduction to the theory of linear nonselfadjoint operators, Translated from the Russian by A. Feinstein. Translations of Mathematical Monographs, Vol. 18, American Mathematical Society, Providence, R. I. , 1969xv+378 39: 7447 0181. 13504 Google Scholar4 Alfred Horn, On the singular values of a product of completely continuous operators, Proc. Nat. Acad. Sci. U. S. A. , 36 (1950), 374–375 13, 565a 0038. 07201 CrossrefISIGoogle Scholar5 R. Horn and, R. Mathias, An analog of the Cauchy-Schwarz inequality for Hadamard products and unitarily invariant norms, Tech. Report, 485, Department of Mathematical Sciences, The Johns Hopkins University, Baltimore, MD, 1988, May Google Scholar6 Fuad Kittaneh, Inequalities for the Schatten p-norm. IV, Comm. Math. Phys. , 106 (1986), 581–585 88j: 47010 0612. 47018 CrossrefISIGoogle Scholar7 A. S. Markus, The eigen- and singular values of the sum and product of linear operators, Russian Math. Surveys, 19 (1964), 92–120 0133. 07205 CrossrefGoogle Scholar8 Albert W. Marshall and, Ingram Olkin, Inequalities: theory of majorization and its applications, Mathematics in Science and Engineering, Vol. 143, Academic Press Inc. Harcourt Brace Jovanovich Publishers, New York, 1979xx+569 81b: 00002 0437. 26007 Google Scholar9 Robert Schatten, Norm ideals of completely continuous operators, Ergebnisse der Mathematik und ihrer Grenzgebiete. N. F. , Heft 27, Springer-Verlag, Berlin, 1960vii+81, New York 22: 9878 0090. 09402 CrossrefGoogle Scholar10 R. C. Thompson, Matrix type metric inequalities, Linear and Multilinear Algebra, 5 (1977/78), 303–319 58: 16725 0433. 15010 CrossrefGoogle Scholar11 R. C. Thompson, Matrix spectral inequalities, Conference Lecture Notes, Mathematical Sciences Lecture Series, Department of Mathematical Sciences, The Johns Hopkins University, Baltimore, MD, 1988, June 20–24 Google Scholar12 Y. Yang, A matrix trace inequality, J. Math. Anal. Appl. , 133 (1988), 573–574 10. 1016/0022-247X (88) 90423-4 89e: 15028 0651. 15018 CrossrefISIGoogle ScholarKeywordscompact operatorsingular valuesunitarily invariant norm Previous article Next article FiguresRelatedReferencesCited ByDetails Introducing discrepancy values of matrices with application to bounding norms of commutatorsLinear Algebra and its Applications, Vol. 651 | 1 Oct 2022 Cross Ref Inequalities for the Kronecker product of matricesAnnals of Functional Analysis, Vol. 13, No. 3 | 21 June 2022 Cross Ref A brief review on Singular Value InequalitiesJournal of Physics: Conference Series, Vol. 2267, No. 1 | 1 May 2022 Cross Ref Some singular value inequalities on majorisation for positive semi-definite matricesIndian Journal of Pure and Applied Mathematics, Vol. 68 | 5 April 2022 Cross Ref Singular value inequalities for operators and matricesAnnals of Functional Analysis, Vol. 13, No. 2 | 11 February 2022 Cross Ref Some Refinements of the Improved Young and Its Reverse 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