Bounded generalized random linear operators
Main Article Content
Abstract
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.
References
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H.W. Engl and W.~Romisch,
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Convergence in distribution,
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Applications},
\newblock Kluwer Academic Publishers, Dordrecht, 1997. $\,$
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maps,
\newblock {\em J.Math.Anal. Appl.}, {\bf 323}:1038--1046, 2006. $\,$
\bibitem{Na}
M.Z. Nashed and H.W. Engl,
\newblock Random generalized inverses and approximate solutions of random
equations,
\newblock in Bharucha-Reid A.T. (Ed.), {\em Approximate Solution of random
equations}, Elsevier, North-Holland, New York-Amsterdam, 1979, pp. 149--210.
$\,$
\bibitem{Sko}
A.V. Skorokhod,
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\newblock Reidel Publishing Company, Dordrecht, 1984. $\,$
\bibitem{Sunder}
V.S. Sunder,
\newblock {\em Functional Analysis: Spectral Theory},
\newblock Birkhauser Verlag, Boston-Berlin, 1998. $\,$
\bibitem{Taraldsen}
G.~Taraldsen,
\newblock {\em Spectral theory of random operators: The energy spectrum of the
quantum electron in a disordered solid},
\newblock {Ph.D.} dissertation, Norwegian University of Science and Technology,
Trondheim, Norway, 1992. $\,$
\bibitem{Thang87}
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\newblock Random operators in banach spaces,
\newblock {\em Probab. Math. Statist.}, {\bf 8}:155--157, 1987. $\,$
\bibitem{Thang98}
D.H. Thang,
\newblock Random mappings on infinite dimensional spaces,
\newblock {\em Stochastics An International Journal of Probability and
Stochastic Processes: formerly Stochastics and Stochastics Reports}, {\bf
64}:51--73, 1998. $\,$
\bibitem{Thang13}
D.H. Thang and P.T. Anh,
\newblock Random fixed points of completely random operators,
\newblock {\em Random Oper. Stoch. Equ.}, {\bf 21}:1--20, 2013. $\,$
\bibitem{th7}
D.H. Thang and N.~Thinh,
\newblock Random bounded operators and their extension,
\newblock {\em Kyushu J.Math.}, {\bf 57}:257--276, 2004. $\,$
\bibitem{thth2}
D.H. Thang and N.~Thinh,
\newblock Generalized random linear operators on a hilbert space,
\newblock {\em Stochastics An International Journal of Probability and
Stochastic Processes: formerly Stochastics and Stochastics Reports}, {\bf
84}(6):1040--1059, 2013. $\,$
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\newblock {\em Journal of Theoretical Probability}, {\bf 27}:676--600, 2014.
$\,$