Title: Some Property of Finite Sum of Weighted Composition and Weighted Frobenius-Perron Operators
Abstract: The study of finite sum of weighted composition operators on <i>L<sup>p</sup></i> - spaces has received considerable attention in 2012. Characterizations, basic properties of this operators have been obtained. Weighted composition operators are a general class of operators and they appear naturally in the study of surjective isometries on most of the function spaces, semi grup theory, dynamic systems etc. This type of operators are a generalization of multiplication operators and composition operators. In this paper the relations among completely continuous and M - weakly compact of finite sum of weighted composition operators between <i>L<sup>p</sup></i>(<i>μ</i>) - spaces described, we also obtain some necessary and sufficient conditions for Fredholmness of the finite sum of weighted composition operators.