A note on Nakano generalized difference sequence space
Awad A. Bakery, Afaf R. Abou Elmatty
Abstract
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 .
Topics & Concepts
MathematicsSequence spaceSequence (biology)Operator (biology)Ideal (ethics)Compact operatorMultiplication operatorEigenvalues and eigenvectorsStrictly singular operatorBanach spaceC0-semigroupMultiplication (music)Pure mathematicsFinite-rank operatorOperator spacePseudo-monotone operatorApproximation propertySpace (punctuation)Type (biology)CombinatoricsHilbert spacePhysicsComputer scienceQuantum mechanicsRepressorBiologyGeneticsEcologyOperating systemPhilosophyExtension (predicate logic)GeneBiochemistryChemistryEpistemologyTranscription factorProgramming languageApproximation Theory and Sequence SpacesAdvanced Banach Space TheoryHolomorphic and Operator Theory