Generalized random linear operators on a Hilbert space

Abstract

In this paper, we are concerned with generalized random linear operators on a separable Hilbert space. Generalized random linear bounded operators, generalized random linear normal operators and generalized random linear self-adjoint operators are defined and investigated. The spectral theorems for generalized random linear normal operators and generalized random linear self-adjoint operators are obtained.

Keywords:

• random operator
• generalized bounded random operator
• generalized random normal operators
• generalized random self-adjoint operators
• random spectral measure

2000 Mathematics Subject Classification::

• 60H025
• 47B80
• 47H40
• 60B11

Acknowledgement

This study was supported by National Foundation for Science and Technology Development (NAFOSTED).