<abstract xmlns="http://www.w3.org/1999/xhtml">

In this paper, we introduce the generalized spaces of the form ℋ(<italic>f, g,</italic> Δ<italic>nm</italic>), where ℋ represents one of the spaces ℓ∞, <italic>c</italic> or <italic>c</italic>0.The köthe duals corresponding to these spaces will be computed and construction of the Schauder bases for ℋ ∈ {<italic>c, c</italic>0} 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∞(<italic>f, g,</italic> Δ<italic>nm</italic>)and <italic>c</italic>0(<italic>f, g,</italic> Δ<italic>nm</italic>)by employing the Hausdorff measure of non-compactness will be determined.
</abstract>

In this paper, we introduce the generalized spaces of the form ℋ(f, g, Δnm), 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, Δnm)and c0(f, g, Δnm)by employing the Hausdorff measure of non-compactness will be determined.

On Some Properties of Difference Operator with Some Characterizations

Basic Science Department, College of Science and Theoretical Studies

Tatra Mountains Mathematical Publications

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

{"article-title":"On Some Properties of Difference Operator with Some Characterizations"}

In this paper, we introduce the generalized spaces of the form ℋ(f, g, Δnm), where ℋ represents one of the spaces ℓ∞, c or c0.The köthe duals corresponding to...

On Some Properties of Difference Operator with Some Characterizations

Published Online: Nov 29, 2022

Page range: 165 - 182

Received: Jul 10, 2022

DOI: https://doi.org/10.2478/tmmp-2022-0013

Keywords
spaces, compact operators, matrix transformations

© 2022 Dowlath Fathima et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

On Some Properties of Difference Operator with Some Characterizations

Published Online: Nov 29, 2022

Page range: 165 - 182

Received: Jul 10, 2022

DOI: https://doi.org/10.2478/tmmp-2022-0013

Keywordsspaces, compact operators, matrix transformations

© 2022 Dowlath Fathima et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
spaces, compact operators, matrix transformations