Rocky Mountain Journal of Mathematics

Compactness of multiplication, composition and weighted composition operators between some classical sequence spaces: A new approach

Ivana Djolović and Eberhard Malkowsky

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Abstract

In a previous paper 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 a previous paper. 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 the previous paper.

Article information

Source
Rocky Mountain J. Math., Volume 47, Number 8 (2017), 2545-2564.

Dates
First available in Project Euclid: 3 February 2018

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1517648599

Digital Object Identifier
doi:10.1216/RMJ-2017-47-8-2545

Mathematical Reviews number (MathSciNet)
MR3760306

Zentralblatt MATH identifier
06840988

Subjects
Primary: 46B45: Banach sequence spaces [See also 46A45]
Secondary: 47B37: Operators on special spaces (weighted shifts, operators on sequence spaces, etc.)

Keywords
Sequence spaces matrix transformations compact operators weighted composition operators

Citation

Djolović, Ivana; Malkowsky, Eberhard. Compactness of multiplication, composition and weighted composition operators between some classical sequence spaces: A new approach. Rocky Mountain J. Math. 47 (2017), no. 8, 2545--2564. doi:10.1216/RMJ-2017-47-8-2545. https://projecteuclid.org/euclid.rmjm/1517648599


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