Generalized Random Spectral Measures

Dang Hung Thang (), Nguyen Thinh () and Tran Xuan Quy ()
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Dang Hung Thang: Hanoi University of Sciences
Nguyen Thinh: Hanoi University of Sciences
Tran Xuan Quy: Thai Nguyen University

Journal of Theoretical Probability, 2014, vol. 27, issue 2, 576-600

Abstract: Abstract In an attempt to examine the random version of the spectral theorem, the notion of random spectral measures and generalized random spectral measures are introduced and investigated. It is shown that each generalized random spectral measure on $$(\mathbb C ,\mathcal{B}(\mathbb C ))$$ admits a modification which is a random spectral measure.

Keywords: Random operators; Random normal operator; Random Hermitian bounded operators; Random projection operator; Random spectral measure; Generalized random spectral measure; Integral with respect to generalized spectral measure; Primary 60H25; Secondary 60H05; 60B11; 45R05 (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/s10959-012-0461-0

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