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.


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


Zbl 0965.46010
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[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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