Norm of matrix operator on Orlicz-binomial spaces and related operator ideal
Volume 23, Issue 4, pp 341--353
http://dx.doi.org/10.22436/jmcs.023.04.07
Publication Date: November 24, 2020
Submission Date: February 11, 2020
Revision Date: March 29, 2020
Accteptance Date: April 08, 2020
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Authors
Taja Yaying
- Department of Mathematics, Dera Natung Govt. College, Itanagar 791111, Arunachal Pradesh, India.
Bipan Hazarika
- Department of Mathematics, Gauhati University, Guwahati 781014, Assam, India.
M. Mursaleen
- Department of Marthematics, Aligarh Muslim University, Aligarh 202002, India.
- Department of Medical Research , China Medical University Hospital, China Medical University (Taiwan), Taichung, Taiwan.
Abstract
The purpose of this article is to introduce Orlicz extension of binomial sequence spaces \(\textbf{b}_{\varphi}^{r,s}\) and investigate some topological and inclusion properties of the new spaces. We give an upper estimation of \(\left\|\textbf{A}\right\|_{\ell_{\varphi},\textbf{b}_{\varphi}^{r,s}} ,\) where \(\textbf{A}\) is the Hausdorff matrix operator or Nörlund matrix operator. A Hardy type formula is established in the case of Hausdorff matrix operator. Finally we introduce operator ideal using the space \(\textbf{b}_{\varphi}^{r,s}\) and the sequence of \(s\)-number function and prove its completeness under certain assumptions.
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ISRP Style
Taja Yaying, Bipan Hazarika, M. Mursaleen, Norm of matrix operator on Orlicz-binomial spaces and related operator ideal, Journal of Mathematics and Computer Science, 23 (2021), no. 4, 341--353
AMA Style
Yaying Taja, Hazarika Bipan, Mursaleen M., Norm of matrix operator on Orlicz-binomial spaces and related operator ideal. J Math Comput SCI-JM. (2021); 23(4):341--353
Chicago/Turabian Style
Yaying, Taja, Hazarika, Bipan, Mursaleen, M.. "Norm of matrix operator on Orlicz-binomial spaces and related operator ideal." Journal of Mathematics and Computer Science, 23, no. 4 (2021): 341--353
Keywords
- Binomial sequence space
- upper bounds
- Hausdorff Matrix
- Orlicz function
- \(s\)-number
- operator ideal
MSC
- 26D15
- 46A45
- 47A30
- 40G05
- 47L20
- 47B06
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