On Absolute Cesa ́ro Series Space And Certain Matrix Transformations

Year 2022, Volume: 12 Issue: 2, 560 - 570, 15.12.2022

Fadime Gökçe

https://doi.org/10.31466/kfbd.1036644

Abstract

On recent paper, the paranormed space |C_(λ,μ) |(p) which is defined as the domain of Cesa ́ro matrix in the Maddox’s space l(p) has been introduced and studied in (Gökçe and Sarıgöl, 2019). In this study, some characterizations of matrix operators from the Absolute Cesa ́ro series space |C_(λ,μ) |(p) to the classical sequence spaces c,c_0,l_∞ are given. Also, it is shown that the matrix operators between the absolute Cesa ́ro series space and the spaces c,c_0,l_∞ are bounded operators. Finally, certain results are obtained as a special case.

Keywords

Absolute summability, matrix transformations, Cesa ́ro matrix, bounded linear operators

Mutlak Cesa ́ro Seri Uzayı Ve Bazı Matris Dönüşümleri

Abstract

Son zamanlarda, Cesa ́ro matrisinin, l(p) Maddox uzayı içinde toplama alanı olarak tanımlanan |C_(λ,μ) |(p) paranormlu uzayı tanıtılmış ve çalışılmıştır, (Gökçe ve Sarıgöl, 2019). Bu çalışmada, |C_(λ,μ) |(p) mutlak Cesa ́ro seri uzayından c,c_0,l_∞ klasik dizi uzaylarına tanımlanan matris operatörlerin karakterizasyonları verilmiştir. Ayrıca mutlak Cesa ́ro seri uzayları ve c,c_0,l_∞ uzayları arasındaki matris operatörlerin sınırlı lineer operatör olduğu gösterilmiştir. Son olarak, özel seçimlerle bazı sonuçlar elde edilmiştir.

Keywords

Mutlak Toplanabilme, matris dönüşümler, Cesa ́ro matrisi, sınırlı lineer operatörler.

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