On Some Properties of Difference Operator with Some Characterizations

Dowlath Fathima; Abdul Hamid Ganie

doi:10.2478/tmmp-2022-0013

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On Some Properties of Difference Operator with Some Characterizations

Tatra Mountains Mathematical Publications

Volume 81 (2022): Issue 1 (November 2022)

By: Dowlath Fathima and Abdul Hamid Ganie

Open Access

|Nov 2022

Abstract

In this paper, we introduce the generalized spaces of the form ℋ(f, g, Δ_n^m), where ℋ represents one of the spaces ℓ_∞, c or c₀.The köthe duals corresponding to these spaces will be computed and construction of the Schauder bases for ℋ ∈ {c, c₀} will be given. Also, some matrix characterizations concerning these spaces will be computed. Moreover, the characterization of some classes of compact operators on the spaces ℓ_∞(f, g, Δ_n^m)and c₀(f, g, Δ_n^m)by employing the Hausdorff measure of non-compactness will be determined.

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Articles in this issue

DOI: https://doi.org/10.2478/tmmp-2022-0013 | Journal eISSN: 1338-9750 (formerly 1210-3195) | Journal ISSN: 1210-3195

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Language: English

Page range: 165 - 182

Submitted on: Jul 10, 2022

Published online: Nov 29, 2022

Published in print: Nov 1, 2022

Published by: Slovak Academy of Sciences, Mathematical Institute

In partnership with: Paradigm Publishing Services

Publication frequency: 1 issue per year

Keywords:

BK spaces,

compact operators,

matrix transformations

MSC:

Primary: 40C05,

Secondary: 46B15, 46B50

Related subjects:

Mathematics,

General mathematics

© 2022 Dowlath Fathima, Abdul Hamid Ganie, published by Slovak Academy of Sciences, Mathematical Institute
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 81 (2022): Issue 1 (November 2022)