Compactness of multiplication, composition and weighted composition operators between some classical sequence spaces: a new approach. (English) Zbl 1481.47044

Djolović, Ivana; Malkowsky, Eberhard

Rocky Mt. J. Math. 47, No. 8, 2545-2564 (2017).

Summary: In [Wei-Hong Wang, “Compact operators of sequence spaces and related problems”, Preprint (2001; per bibl.)], the author studied the compactness of multiplication, composition and weighted composition operators among some sequence spaces. We were motivated by these results and present two different approaches for obtaining some of the results in [loc. cit.]. The first approach is to apply the theory of matrix transformations and the Hausdorff measure of noncompactness, and the second one is to use known results on multiplier spaces and the Hausdorff measure of noncompactness. We also use our techniques and methods from our proofs of the existing results to establish some new results related to the class of Fredholm operators and some classes of operators considered here and in [loc. cit.].

MSC:

47B37	Linear operators on special spaces (weighted shifts, operators on sequence spaces, etc.)
47B33	Linear composition operators
46B45	Banach sequence spaces

Keywords:

sequence spaces; matrix transformations; compact operators; weighted composition operators; Hausdorff measure of noncompactness; Fredholm operators