Some Property of Finite Sum of Weighted Composition and Weighted Frobenius-Perron Operators

Abolghasem Alishahi

doi:10.11648/j.ijtam.20190504.12

Abstract

The study of finite sum of weighted composition operators on Lp - 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 Lp(μ) -‎ spaces described, we also obtain some necessary and sufficient conditions for Fredholmness of the finite sum of weighted composition operators.

Highlights

Weighted composition operators are a general class of operators
There are many great papers on the investigation of weighted composition operators acting on the spaces of measurable functions
The finite sum of weighted composition operators were studied on -spaces [9, 15]

Summary

Introduction

Weighted composition operators are a general class of operators. There are many great papers on the investigation of weighted composition operators acting on the spaces of measurable functions. The finite sum of weighted composition operators were studied on -spaces [9, 15]. We give some sufficient and necessary conditions for completely continuous, ' -weakly compact and Fredholmness of finite sum of weighted composition operator " on Σ and finite sum of weighted Frobeniuse-Perron operator on Σ. Meyer - Nieberg [1] in the study of Riesz spaces In this theorem we give some necessary and sufficient conditions for " to be completely continuous as an operator from into. Since sequence S [ W ∈N has no subsequence that converges to zero, Sn; [ ⊆ is finite and so k [ ∩ l 0 for sufficiently large n and.

Fredholmness of the Finite Sum of Wieghted Composition Operators

Conclusion