## Rocky Mountain Journal of Mathematics

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

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

Ivana Djolović and Eberhard Malkowsky

#### 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