Basic Properties of Finite Sum of Weighted Composition Operators


Abolghasem Alishahi, Saeedeh Shamsigamchi, Ali Ebadian




In this paper,we continue the study of finite sum of weighted composition operators between different Lp-spaces that was investigated by Jabbarzadeh and Estaremi in 2012. Indeed, we first obtain some necessary and sufficient conditions for boundedness of the finite sums of weighted composition operators between distinct Lp-spaces. In the sequel, we investigate the compactness of finite sum of weighted composition operators. By using theorems of boundedness and compactness, we estimate the essential norms of these operators. Finally, some examples to illustrate the main results are given.