Conditional Weighted Operators in $L^{2}(\Sigma)$-Semi-Hilbertian space

Document Type : Original Paper

Author

Lorestan University, Department of Mathematics

Abstract

In this paper, we discuss matrix theoretic characterization for weighted conditional operators by properties of conditional expectation operator in some operator classes on $L^{2}(\Sigma)$-semi-Hilbertian space such as self-adjoint, isometry and normal classes of these type operators on this space. Also, we consider the matrix representation of the Moore-Penrose inverse for these types of operators. We also gave examples to show our results.

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