Some New Paranormed Sequence Spaces and $\alpha-$ Core

TL;DR

This paper introduces new paranormed sequence spaces constructed via matrix methods, explores their duals and bases, characterizes matrix transformations to classical spaces, and defines the alpha-core with related inclusion theorems.

Contribution

It presents novel paranormed sequence spaces based on matrix combinations, along with their duals, bases, and transformation properties, and introduces the alpha-core concept with theoretical results.

Findings

Defined new paranormed sequence spaces using matrix methods

Computed duals and bases for these spaces

Characterized matrix transformations to classical sequence spaces

Abstract

In this study, we define new paranormed sequence spaces by combining a double sequential band matrix and a diagonal matrix. Furthermore, we compute the $\alpha-,\beta-$ and $\gamma-$ duals and obtain bases for these sequence spaces. Besides this, we characterize the matrix transformations from the new paranormed sequence spaces to the spaces $c_{0}(q),c(q),\ell(q)$ and $\ell_{\infty}(q)$. Finally, $\alpha-core$ of a complex-valued sequence has been introduced, and we prove some inclusion theorems related to this new type of core.