Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

Operator versions of the Kantorovich inequality

Author(s): P. G. Spain
Journal: Proc. Amer. Math. Soc. 124 (1996), 2813-2819.
MSC (1991): Primary 47A63; Secondary 15A45, 65F65
MathSciNet review: 1328379
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Abstract: The Operator Kantorovich Inequality

$\begin{displaymath}(R^2 - r^2) \, u^* (a^* a) \, u \le R^2 \, (u^* a^* u) (u^* a u) \end{displaymath}$

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:

[BP]: JK Baksalary & S Puntanen, Generalized matrix versions of the Cauchy-Schwarz and Kantorovich inequalities, Aequationes Mathematicae 41 (1991), 103-110. MR 91k:15038
[GR]: W Greub & W Rheinboldt, On a generalization of an inequality of L.V. Kantorovich, Proc American Math Soc 10 (1959), 407-415. MR 21:3774
[K]: L V Kantorovich, Functional analysis and applied mathematics (Russian), Uspekhi Mat Nauk (NS) 3 (1948), 89-185. MR 10:380a
[S]: W G Strang, On the Kantorovich Inequality, Proc American Math Soc 11 (1959) 468. MR 22:2904

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