Inequalities of Schwarz and Hölder type for random operators

Hegerfeldt, Gerhard C. (1985) Inequalities of Schwarz and Hölder type for random operators. Journal of Mathematical Physics, 26 (7). pp. 1576-1577. ISSN 0022-2488 http://resolver.caltech.edu/CaltechAUTHORS:HEGjmp85

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Abstract

Let A and B be random operators on a Hilbert space, and let 〈 〉 denote averages (expectations). We prove the inequality ||〈A*B〉||≤||〈A*A〉||^1/2||〈B*B〉||^1/2. A generalized Hölder inequality involving traces is also proved.

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Copyright © 1985 American Institute of Physics. Received 13 November 1984; accepted 4 January 1985. I would like to thank Mary Beth Ruskai for pointing out Ref. 2. My thanks also go to W.A.J. Luxemburg and B. Simon for the hospitality extended to me at Caltech. This work was supported in part by the Stiftung Volkswagenwerk.

Funders:

Funding Agency	Grant Number
Stiftung Volkswagenwerk	UNSPECIFIED

Subject Keywords:

MATHEMATICAL OPERATORS, ALGEBRA, HILBERT SPACE, EXPECTATION VALUE, COMMUTATION RELATIONS, INTEGRALS, CONVERGENCE, FUNCTIONAL ANALYSIS

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28 Oct 2008 18:41

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