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Random spectral theorems of self-adjoint random linear operators on complete complex random inner product modules. (English) Zbl 1278.47045

The paper under review continues the study initiated by T.-X. Guo [Acta Anal. Funct. Appl. 1, No. 2, 160–184 (1999; Zbl 0965.46010)]. The author proves some properties of the spectrum of bounded random linear operators. For self-adjoint operators, such a spectrum is a subset of \(L^0({\mathcal F},R)\), and the author gives, e.g., lower and upper bounds for its elements. If the base probability space is trivial, the obtained results reduce to the classical case.

MSC:

47B80 Random linear operators
46H25 Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX)
47S50 Operator theory in probabilistic metric linear spaces

Citations:

Zbl 0965.46010
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References:

[1] Dunford N, Linear Operators, Part I (1957)
[2] DOI: 10.1016/j.jfa.2008.11.015 · Zbl 1180.46055
[3] Guo TX, Acta Anal. Funct. Appl. 1 pp 160– (1999)
[4] DOI: 10.1016/j.jfa.2010.02.002 · Zbl 1198.46058
[5] DOI: 10.1007/s11425-011-4189-6 · Zbl 1238.46058
[6] DOI: 10.1007/s11425-009-0149-9 · Zbl 1193.46048
[7] DOI: 10.1016/j.na.2009.02.038 · Zbl 1184.46068
[8] Tang YH, Complete random normed algebras · Zbl 1299.46050
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