scholarly journals Multiplication Operators on Orlicz Generalized Difference (sss)

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Awad A. Bakery ◽  
OM Kalthum S. K. Mohamed
Keyword(s):  
Sequence Space ◽  
Sufficient Conditions ◽  
Multiplication Operators ◽  
Difference Sequence ◽  
Geometrical Structures ◽  
Difference Sequence Space

In this article, we inspect the sufficient conditions on the Orlicz generalized difference sequence space to be premodular Banach (sss). We look at some topological and geometrical structures of the multiplication operators described on Orlicz generalized difference prequasi normed (sss).

scholarly journals A note on Nakano generalized difference sequence space

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Awad A. Bakery ◽  
Afaf R. Abou Elmatty
Keyword(s):  
Sequence Space ◽  
Sufficient Conditions ◽  
Multiplication Operator ◽  
Operator Ideal ◽  
Difference Sequence ◽  
Geometrical Structures ◽  
Difference Sequence Space ◽  
Necessary And Sufficient ◽  
Special Space ◽  
Type Sequence

Abstract In this paper, we investigate the necessary conditions on any s-type sequence space to form an operator ideal. As a result, we show that the s-type Nakano generalized difference sequence space X fails to generate an operator ideal. We investigate the sufficient conditions on X to be premodular Banach special space of sequences and the constructed prequasi-operator ideal becomes a small, simple, and closed Banach space and has eigenvalues identical with its s-numbers. Finally, we introduce necessary and sufficient conditions on X explaining some topological and geometrical structures of the multiplication operator defined on X.

scholarly journals Multiplication Operators on Weighted Nakano (sss)

2020 ◽  
Vol 2020 ◽  
pp. 1-7 ◽  
Author(s):  
Awad A. Bakery ◽  
Afaf R. Abou Elmatty ◽  
OM Kalthum S. K. Mohamed
Keyword(s):  
Sequence Space ◽  
Sufficient Conditions ◽  
Multiplication Operators ◽  
Geometrical Structures

In this article, we investigate the sufficient conditions on weighted Nakano sequence space to be premodular Banach (sss). We examine some topological and geometrical structures of the multiplication operators defined on weighted Nakano prequasi-normed (sss).

scholarly journals Orlicz Generalized Difference Sequence Space and the Linked Pre-Quasi Operator Ideal

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Awad A. Bakery ◽  
OM Kalthum S. K. Mohamed
Keyword(s):  
Banach Space ◽  
Sequence Space ◽  
Necessary Conditions ◽  
Sufficient Conditions ◽  
Operator Ideal ◽  
Difference Sequence ◽  
Difference Sequence Space ◽  
Special Space

In this article, the necessary conditions on s-type Orlicz generalized difference sequence space to generate an operator ideal have been examined. Therefore, the s-type Orlicz generalized difference sequence space which fails to generate an operator ideal has been shown. We investigate the sufficient conditions on this sequence space to be premodular Banach special space of sequences, and the constructed pre-quasi operator ideal becomes small, simple, closed, Banach space and has eigenvalues identical with its s-numbers.

scholarly journals NEW GENERALIZED CIESARO SPACE WITH SOME TOPOLOGICAL PROPERTIES

2021 ◽  
pp. 253-262
Author(s):  
Rayees Ahmad
Keyword(s):  
Sequence Space ◽  
Subject Classification ◽  
Difference Sequence ◽  
Topological Properties ◽  
Inclusion Relations ◽  
Difference Sequence Space

The sequence space introduced by M. Et and have studied its various properties. The aim of the present paper is to introduce the new pranormed generalized difference sequence space. and , We give some topological properties and inclusion relations on these spaces. 2010 AMS Mathematical Subject Classification: 46A45; 40C05.

On New Difference Sequence Space and Their Generalised Almost Statistical Convergence

2020 ◽  
pp. 212-219
Author(s):  
Ajaya Kumar Singh
Keyword(s):  
Sequence Space ◽  
Statistical Convergence ◽  
Convergent Sequence ◽  
Difference Sequence ◽  
Almost Convergence ◽  
Topological Properties ◽  
Statistical Limit ◽  
Difference Sequence Space ◽  
Limit Functional ◽  
Convergent Sequences

The object of the present paper is to introduce the notion of generalised almost statistical (GAS) convergence of bounded real sequences, which generalises the notion of almost convergence as well as statistical convergence of bounded real sequences. We also introduce the concept of Banach statistical limit functional and the notion of GAS convergence mainly depends on the existence of Banach statistical limit functional. We prove the existence of Banach statistical limit functional. Also, the existence GAS convergent sequence, which is neither statistical convergent nor almost convergent. Lastly, some topological properties of the space of all GAS convergent sequences are investigated.

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