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Bounds and positivity conditions for operator valued functions in a Hilbert lattice

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Abstract

In this paper we investigate regular functions of a bounded operator A acting in a Hilbert lattice and having the form A=D + T, where T is a positive operator and D is a selfadjoint operator whose resolution of the identity P(t) \((a\le s \le b)\) has the property \(P(s_2)-P(s_1)\;\;(s_1<s_2)\) are non-negative in the sense of the order. Upper and lower bounds and positivity conditions for the considered operator valued functions are derived. Applications of the obtained estimates to functions of integral operators, partial integral operators, infinite matrices and differential equations are also discussed.

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  1. Department of Mathematics, Ben Gurion University of the Negev, P.O. Box 653, 84105, Beer-Sheva, Israel

    Michael Gil’

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  1. Michael Gil’
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Correspondence to Michael Gil’.

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Gil’, M. Bounds and positivity conditions for operator valued functions in a Hilbert lattice. Positivity 17, 407–414 (2013). https://doi.org/10.1007/s11117-012-0176-6

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  • DOI: https://doi.org/10.1007/s11117-012-0176-6

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