On Random Normal Operators and Their Spectral Measures

Păstorel Gaşpar ()
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Păstorel Gaşpar: “Aurel Vlaicu” University

Journal of Theoretical Probability, 2019, vol. 32, issue 4, 2088-2110

Abstract: Abstract The main aim of this paper is to introduce and study the subclass of not necessarily continuous, normal random operators, establishing connections with other subclasses of random operators, as well as with the existing concept of random projection operator-valued measure. Hence, after recalling some basic facts regarding random operators on a complex separable Hilbert space, theorems about transforming the class of not necessarily continuous decomposable random operators into the class of purely contractive random operators are proved. These are applied to obtain integral representations for not necessarily continuous normal or self-adjoint random operators on a Hilbert space with respect to the corresponding random projection operator-valued measures.

Keywords: Stochastic mappings; Random operator; Normal random operator; Self-adjoint random operator; Random projection operator-valued measure; Integral representation; 60G60; 46F12; 42B10 (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s10959-018-0870-9

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