On the generalized Cesàro sequence spaces and some of their properties

Authors

• UĞUR GÖNÜLLÜFollow
• FARUK POLATFollow
• MARTIN RICHARD WEBERFollow

Author ORCID Identifier

FARUK POLAT: 0000-0002-4107-137X

UĞUR GÖNÜLLÜ: 0000-0002-4508-4100

MARTIN WEBER: 0000-0002-0699-5091

Abstract

Let C_t = (c_nm)_n,m∈ℕ denote the generalized Cesàro matrix defined by c_nm = t^n−m/n for m ≤ n and t ∈ [0, 1], and c_nm = 0 otherwise. For each q ∈ [1, ∞), the associated generalized Cesàro sequence spaces ces_q^t are introduced. These spaces form Banach lattices under the coordinatewise order, equipped with a naturally defined order continuous norm. We prove that ces_q^t = ces_q⁰ for all t ∈ [0, 1) and q ∈ [1, ∞), implying that the space ces_q^t is a weighted ℓ_q space with equivalent norm. Furthermore, we examine the inclusion relationships between ces_q and ces_q^t, and establish that ces_q is a proper subspace of ces_q^t whenever t ∈ [0, 1). Finally, we explore various geometric properties of these spaces, including the characterization of extreme points of the unit ball, strict convexity, (nearly) uniform convexity, (nearly) uniform smoothness, and property (β).

DOI

10.55730/1300-0098.3775

Keywords

Generalized Cesàro sequence spaces, geometric property, Banach lattice

First Page

933

Last Page

949

Publisher

The Scientific and Technological Research Council of Türkiye (TÜBİTAK)

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Recommended Citation

GÖNÜLLÜ, U, POLAT, F, & WEBER, M. R (2026). On the generalized Cesàro sequence spaces and some of their properties. Turkish Journal of Mathematics 50 (5): 933-949. https://doi.org/10.55730/1300-0098.3775