Mersenne Matrix Operator and Its Application in $p-$Summable Sequence Space
Serkan Demiriz, Sezer Erdem
Abstract
In this study, it is introduced the regular Mersenne matrix operator which is obtained by using Mersenne numbers and examined sequence spaces described as the domain of this matrix in the space of $p$-summable sequences for $1\leq p \leq \infty$. After that, it investigated some properties and inclusion relations, established the Schauder basis, and stated $\alpha-$, $\beta-$, and $\gamma-$duals of the aforementioned spaces. Additionally, it is characterized by the matrix classes from newly described spaces to classical sequence spaces. Finally, we studied the compactness of matrix operators on related sequence spaces.
Topics & Concepts
Mersenne primeSequence (biology)MathematicsSchauder basisDual polyhedronMatrix (chemical analysis)Sequence spaceOperator (biology)Space (punctuation)Basis (linear algebra)Pure mathematicsCombinatoricsBanach spaceComputer scienceGeometryRepressorTranscription factorOperating systemBiologyBiochemistryComposite materialMaterials scienceGeneChemistryGeneticsApproximation Theory and Sequence SpacesAdvanced Banach Space TheoryFuzzy and Soft Set Theory