Generalized random linear operators on a Hilbert space

Thang, Dang Hung; Thinh, Nguyen An

doi:10.1080/17442508.2012.736995

Cited by 10 publications

(11 citation statements)

References 15 publications

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“…In this section, some definitions and typical results on random bounded operator, bounded generalized random linear operator are listed and discussed. For more details, we refer the reader to [14,17,18,19].…”

Section: Random Bounded Operators and Bounded Generalized Random Linementioning

confidence: 99%

“…It should be noted that the notion of g.r.l.o. has been introduced in [18] where X, Y are Hilbert spaces.…”

Section: A Generalized Random Linear Operatormentioning

confidence: 99%

“…Research in theory of random mappings has been carried out in many directions including random linear mappings which provide a framework of stochastic integral, infinite random matrix (see e.g. [2,5,11], [14][15][16][17][18][19]), random fixed points of random operators, semi groups of random operators and random operator equations (e.g. [3], [6], [10]- [16] and references therein).…”

Section: Introduction mentioning

confidence: 99%

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Bounded generalized random linear operators

Thinh¹

2017

MaP

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In this paper we are concerned with bounded generalized random linear operators. It is shown that each bounded generalized random linear operator can be seen as a set-valued random variable. The properties of some special bounded generalized random linear operators are given also. As an application the notion of random resolvent set of a generalized random linear operator is introduced and investigated.

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Section: Random Bounded Operators and Bounded Generalized Random Linementioning

confidence: 99%

“…It should be noted that the notion of g.r.l.o. has been introduced in [18] where X, Y are Hilbert spaces.…”

Section: A Generalized Random Linear Operatormentioning

confidence: 99%

Section: Introduction mentioning

confidence: 99%

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Bounded generalized random linear operators

Thinh¹

2017

MaP

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“…The remainder of this section contains some general concepts and basic results especially regarding continuous random operators and generalized random operators. Also selected specific results from [7,13,[23][24][25] (regarding decomposable random operators and the random adjoint) are reformulated and completed in a way to suit our present development.…”

Section: Introductionmentioning

confidence: 99%

On Random Normal Operators and Their Spectral Measures

Gaşpar

2018

J Theor Probab

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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 operatorvalued 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.

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“…The random operator theory is one of the branches of the theory of random processes and functions; its creation is a natural step in the development of random analysis. Research in theory of random operators has been carried out in many directions such as random fixed points of random operators, random operator equations, random linear operators (see [1][2][3][4]).…”

Section: Introductionmentioning

confidence: 99%