A NOTE ON RADON-NIKODYM THEOREM FOR OPERATOR VALUED MEASURES AND ITS APPLICATIONS

- Journal title : Communications of the Korean Mathematical Society
- Volume 28, Issue 2, 2013, pp.285-295
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/CKMS.2013.28.2.285

Title & Authors

A NOTE ON RADON-NIKODYM THEOREM FOR OPERATOR VALUED MEASURES AND ITS APPLICATIONS

Ahmed, Nasiruddin;

Ahmed, Nasiruddin;

Abstract

In this note we present sufficient conditions for the existence of Radon-Nikodym derivatives (RND) of operator valued measures with respect to scalar measures. The RND is characterized by the Bochner integral in the strong operator topology of a strongly measurable operator valued function with respect to a nonnegative finite measure. Using this result we also obtain a characterization of compact sets in the space of operator valued measures. An extension of this result is also given using the theory of Pettis integral. These results have interesting applications in the study of evolution equations on Banach spaces driven by operator valued measures as structural controls.

Keywords

space of operator valued measures;strong operator topology;Radon-Nikodym theorem;RNP;Bochner and Pettis integrals;evolution equations on Banach spaces;

Language

English

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