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

Tang, Yuehan

Linear Multilinear Algebra 61, No. 3, 409-416 (2013).

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.

Reviewer: Andrzej Nowak (Katowice)

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

Keywords:

random normed module; random normed algebra; random C\(^\ast\)-algebra; random linear operator; self-adjoint; random spectral theorem

Citations:

Zbl 0965.46010

References:

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