On sequence space derived by the domain of q-Cesàro matrix in ℓ space and the associated operator ideal

By T. Yaying, Bipan Hazarika, M. Mursaleen. 2021

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Abstract We study the sequence space X p q obtained by using the domain of q-analogue of the Cesaro matrix C ( q ) = ( c i j q ) defined by c i j q = { q j − 1 [ i ] q ( 1 ≤ j ≤ i ) , 0 ( j > i ) , where the notation [ i ] q has the usual meaning. We study some topological properties and inclusion relations of the space X p q , obtain its Schauder basis and α−, β− and γ−duals. We characterize certain matrix classes related to the space X p q . Finally, we introduce a class X p ( s ) ( q ) of s-type X p q operators for 1 p ∞ using the newly defined space.

Subfields: Mathematical Physics, Numerical Analysis, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/c7a41aa68741e92625a80a9cfa96a7dd26d42271