A note on the some geometric properties of the sequence spaces defined by Taylor method

TL;DR

This paper explores geometric properties of sequence spaces derived from the Taylor method, establishing their structure, duals, and conditions under which they form Hilbert spaces, thus extending classical sequence space theory.

Contribution

It introduces a new sequence space based on the Taylor method, analyzes its structure, duals, and geometric properties, and characterizes matrix classes related to this space.

Findings

The new space is isomorphic to all absolutely p-summable sequences.

It is a Hilbert space when p=2.

Dual spaces and matrix class characterizations are provided.

Abstract

In this paper, it was obtained the new matrix domain with the well known classical sequence spaces and an infinite matrix. The Taylor method which known then as the circle method of order r (0 < r < 1), as an infinite matrix for the matrix domain is used. Newly constructed space is isomorphic copy of the spaces of all absolutely p-summable sequences. It is well known that Hilbert space have the nicest geometric properties. Then, it is proved that the new space is a Hilbert space for p = 2. Further, it was computed dual spaces and characterized some matrix classes of the new Taylor space in the table form. Section 3 is devoted some geometric properties of Taylor space.