Domain of difference matrix of order one in some spaces of double sequences
Serkan Demiriz, Osman Duyar

TL;DR
This paper introduces new double sequence spaces based on difference transformations, explores their properties including duals, and characterizes matrix transformations between these spaces, expanding the theoretical framework of sequence space analysis.
Contribution
It defines several new double sequence spaces related to difference transformations, proves they are Banach spaces, and characterizes their duals and matrix transformations, which is a novel extension in the field.
Findings
Spaces are Banach spaces.
Determined alpha-dual and beta(v)-dual of specific spaces.
Characterized classes of matrix transformations.
Abstract
In this study, we define the spaces and of double sequences whose difference transforms are bounded , convergent in the Pringsheim's sense, null in the Pringsheim's sense, both convergent in the Pringsheim's sense and bounded, regularly convergent and absolutely summable, respectively, and also examine some inclusion relations related to those sequence spaces. Furthermore, we show that these sequence spaces are Banach spaces . We determine the alpha-dual of the space and the dual of the space of double sequences, where . Finally, we characterize the classes for of four dimensional matrix transformations, where is any…
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Taxonomy
TopicsApproximation Theory and Sequence Spaces · Advanced Topics in Algebra · Advanced Banach Space Theory
