New additive results for Cauchy dual and MP$-$inverse OF Weighted composition operators

Abstract

In this paper, we prove some basic results for Cauchy dual of
weighted composition operators. Also we introduce some new classes
of operators, called $\dag$-hyponormal, $\dag$-quasi-hyponormal, and
we provide necessary and sufficient conditions for Cauchy dual and
MP$-$inverse of weighted composition operators on $L^{2}(\Sigma)$ to
belong to these classes . In addition, we study the complex symmetry
of these types of operators. Moreover, some
examples are provided to illustrate the obtained results