# Almost absolute weighted summability with index k

## TL;DR

This paper introduces a generalized space of almost summable series using weighted means, explores its topological properties, relationships with classical spaces, and characterizes related matrix operators.

## Contribution

It extends the space of almost summable series with weights and factors, analyzing its structure and operator behavior, which was not previously studied.

## Key findings

- The generalized space has specific topological properties.
- Relations between the new space and classical sequence spaces are established.
- Matrix operators acting on the space are characterized.

## Abstract

The space $\widehat{\ell }_k$ of absolutely almost convergent series was introduced and studied by Das et al [4]; which plays an important role in summability theory, approximation theory, Fourier analysis, etc. In the present paper we generalize the space making use of some factors and weighted mean transformations, investigate its topological structures and relations between classical sequence spaces. Also we characterize certain matrix operators on it.