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Zbl 0864.47006
Spain, P.G.
Operator versions of the Kantorovich inequality. (English)
[J] Proc. Am. Math. Soc. 124, No.9, 2813-2819 (1996). ISSN 0002-9939; ISSN 1088-6826/e

Summary: The operator Kantorovich inequality $$(R^2-r^2) u^*(a^*a)u\leq R^2(u^*a^*u)(u^*au)$$ holds for a wide class of operators $a$ on a Hilbert space ${\cal H}$ and all operators $u:{\cal K}\to{\cal H}$ for which $[a]u$ is a partial isometry, $[a]$ being the range projection of $a$.

MSC 2000:: *47A63 Operator inequalities, etc.
15A45 Miscellaneous inequalities involving matrices

Keywords: Cauchy-Schwarz inequality; operator Kantorovich inequality; partial isometry; range projection

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Zentralblatt MATH Berlin [Germany]