Genelleştirilmiş Mutlak Cesàro Seri Uzaylarında Nonkompaktlık Ölçüsünün Uygulamaları

Yıl 2020, Cilt: 10 Sayı: 1, 60 - 73, 15.06.2020

G. Canan H. Güleç

https://doi.org/10.31466/kfbd.723446

Cited By: 2

Öz

Bu çalışmada, |C_(λ,μ) |_p (p≥1) genelleştirilmiş mutlak Cesàro seri uzaylarından l_∞,c ve c_0 klasik dizi uzaylarına bazı matris dönüşümleri karakterize edilmiştir. Bunun yanı sıra, bu matris dönüşümlerine karşılık gelen sınırlı lineer operatörlerin normları için bazı özdeşlikler veya tahminler verilmiştir. Ayrıca, nonkompaktlık Hausdorff ölçüsünün uygulaması ile bu operatörlerin kompakt olması için gerek ve yeter şartlar elde edilmiştir.

Anahtar Kelimeler

Dizi Uzayları, Matris Operatörler, BK Uzayları, Kompakt Operatörler, Hausdorff Nonkompaktlık Ölçüsü

Applications of Measure of Noncompactness in the Series Spaces of Generalized Absolute Cesàro Means

Öz

In this study, we characterize some matrix transformations from the generalized absolute Cesàro series spaces |C_(λ,μ) |_p (p≥1) to the classical sequence spaces l_∞,c and c_0. Besides this, we obtain some identities or estimates for the norms of the bounded linear operators corresponding these matrix transformations. Further, by applying the Hausdorff measure of noncompactness, we give the necessary and sufficient conditions for such operators to be compact.

Anahtar Kelimeler

Sequence Spaces, Matrix Operators, BK Spaces, Compact Operators, Hausdorff Measure of Noncompactness

Kaynakça

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