Operator versions of the Kantorovich inequality

Spain, P.

doi:10.1090/S0002-9939-96-03424-7

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 $a.$

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