Operator versions of the Kantorovich inequality
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- by P. G. Spain
- Proc. Amer. Math. Soc. 124 (1996), 2813-2819
- DOI: https://doi.org/10.1090/S0002-9939-96-03424-7
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Abstract:
The Operator Kantorovich Inequality \[ (R^2 - r^2) u^* (a^* a) u \le R^2 (u^* a^* u) (u^* a u) \] holds for a wide class of operators $a$ on a Hilbert space $\mathcal {H}$ and all operators $u: \mathcal {K}\to \mathcal {H}$ for which $[a] u$ is a partial isometry, $[a]$ being the range projection of $a.$References
- J. K. Baksalary and S. Puntanen, Generalized matrix versions of the Cauchy-Schwarz and Kantorovich inequalities, Aequationes Math. 41 (1991), no. 1, 103–110. MR 1088268, DOI 10.1007/BF02227445
- Werner Greub and Werner Rheinboldt, On a generalization of an inequality of L. V. Kantorovich, Proc. Amer. Math. Soc. 10 (1959), 407–415. MR 105028, DOI 10.1090/S0002-9939-1959-0105028-3
- Morgan Ward, Ring homomorphisms which are also lattice homomorphisms, Amer. J. Math. 61 (1939), 783–787. MR 10, DOI 10.2307/2371336
- G. Strang, On the Kantorovich inequality, Proc. Amer. Math. Soc. 11 (1960), 468. MR 112046, DOI 10.1090/S0002-9939-1960-0112046-6
Bibliographic Information
- P. G. Spain
- Affiliation: Department of Mathematics, University of Glasgow, Glasgow G12 8QW, Scotland
- Email: pgs@maths.gla.ac.uk
- Received by editor(s): March 23, 1995
- Communicated by: Palle E. T. Jorgensen
- © Copyright 1996 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 124 (1996), 2813-2819
- MSC (1991): Primary 47A63; Secondary 15A45, 65F65
- DOI: https://doi.org/10.1090/S0002-9939-96-03424-7
- MathSciNet review: 1328379