Journal of the
Korean Mathematical Society
JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

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J. Korean Math. Soc. 2016; 53(2): 347-362

Printed March 1, 2016

https://doi.org/10.4134/JKMS.2016.53.2.347

Copyright © The Korean Mathematical Society.

Abstract random linear operators on probabilistic unitary spaces

Tran Xuan Quy, Dang Hung Thang, and Nguyen Thinh

Thai Nguyen University, Hanoi University of Sciences, Hanoi University of Sciences

Abstract

In this paper, we are concerned with abstract random linear operators on probabilistic unitary spaces which are a generalization of generalized random linear operators on a Hilbert space defined in \cite{Thang2012}. The representation theorem for abstract random bounded linear operators and some results on the adjoint of abstract random linear operators are given.

Keywords: probabilistic linear space, probabilistic unitary space, probabilistic Hilbert space, abstract random linear operator, abstract random bounded linear operator, abstract random symmetric operator, abstract random self-adjoint operator, abstract random norm

MSC numbers: 60H025, 47B80, 47H40, 60B11

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