Some results on cauchy dual of conditional type operators

Abstract

. In this paper, we discuss measure theoretic some characterizations of the notion of Cauchy dual for Lambert conditional operators in some operator classes on L 2 ( Σ ) such as, n - normal, n -quasi-normal, n -power †-normal, n -power †-quasi-normal. Moreover, the relations between these classes and some basic properties of these operators are studied. Finally, using the matrix representation, some examples are provided to illustrate the obtained results.