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

Bounds and positivity conditions for operator valued functions in a Hilbert lattice 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

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

, Volume 17 (3) – Apr 10, 2012
8 pages

/lp/springer_journal/bounds-and-positivity-conditions-for-operator-valued-functions-in-a-UOOwTfP0ke
Publisher
Springer Basel
Subject
Mathematics; Fourier Analysis; Operator Theory; Potential Theory; Calculus of Variations and Optimal Control; Optimization; Econometrics
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1007/s11117-012-0176-6
Publisher site
See Article on Publisher Site

### 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.

### Journal

PositivitySpringer Journals

Published: Apr 10, 2012

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