Tbilisi Mathematical Journal

Compact and matrix operators on the space $\left\vert A_{f}^{\theta }\right\vert _{k}$

Fadime Gökçe and G. Canan Hazar Güleç

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Abstract

In this study, we introduce a new space $\left\vert A_{f}^{\theta}\right\vert_{k}$ by using factorable matrix and investigate its certain topological and algebraic structures where $\theta$ is a positive sequence. Also, we characterize some matrix operators on this space and determine their norms and the Hausdorff measure of noncompactness. In the particular case, we get some well known results.

Article information

Source
Tbilisi Math. J., Volume 12, Issue 4 (2019), 1-13.

Dates
Received: 21 January 2019
Accepted: 15 September 2019
First available in Project Euclid: 3 January 2020

Permanent link to this document
https://projecteuclid.org/euclid.tbilisi/1578020563

Digital Object Identifier
doi:10.32513/tbilisi/1578020563

Mathematical Reviews number (MathSciNet)
MR4047571

Subjects
Primary: 40C05: Matrix methods
Secondary: 40D25: Inclusion and equivalence theorems 40F05: Absolute and strong summability (should also be assigned at least one other classification number in Section 40) 46A45: Sequence spaces (including Köthe sequence spaces) [See also 46B45]

Keywords
matrix transformations factorable matrices sequence spaces Hausdorff measure of noncompactness norms compact operators

Citation

Gökçe, Fadime; Güleç, G. Canan Hazar. Compact and matrix operators on the space $\left\vert A_{f}^{\theta }\right\vert _{k}$. Tbilisi Math. J. 12 (2019), no. 4, 1--13. doi:10.32513/tbilisi/1578020563. https://projecteuclid.org/euclid.tbilisi/1578020563


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