A New Outlook for Almost Convergent Sequence Spaces

Yıl 2018, Cilt: 39 Sayı: 1, 34 - 46, 16.03.2018

Murat Candan

https://doi.org/10.17776/csj.383311

Cited By: 1

Öz

The
point standing out in the present paper is the sequence spaces ,  and produced
by the domain of the infinite matrix ,
which is defined in the previous study of Candan [2], where the spaces ,  and ,
respectively, are as presented by G.G. Lorentz utilizing the issue of the
Banach limits (Acta.  Math.  80. 
1948, 167-190), andis
the double sequential band matrix and G is the generalized weighted mean.
Firstly, it is shown that aforementioned spaces are linearly isomorhic to the
spaces ,  and ,
respectively. In addition to these, andduals
of the spaces  and  are given. Beyond them, the classes  and   of infinite matrices are characterized, where
 is a given sequence space.

Anahtar Kelimeler

Almost convergence, Generalized weigheted mean, Sequence space, , Matrix transformations

Hemen Hemen Yakınsak Dizi Uzaylar için Yeni Bir Bakış

Öz

Banach limiti (Acta.  Math.  80. 
1948, 167-190) kavramını kullanarak G.G. Lorentz hemen hemen
yakınsak dizilerin  uzayını tanımladı. Bu çalışmada öne çıkan
nokta ,  ve  uzaylarının 
Candan [2] tarafından tanımlanan  matris etki alanında olan ,  ve  uzaylarını tanımlamaktır. Burada ikili
dizisel band matrisi de
genelleştirilmiş ağırlıklı ortalamayı göstermektedir. Çalışmada öncelikle ,  ve uzaylarının
sırası ile ,  ve uzaylarına
lineer izomorf oldukları gösterildikten sonra  ve uzaylarının
sırası ile vedualleri
elde edilmiştir. Son bölümde de verilen
herhangi bir dizi uzayı olmak üzere  ve matris sınıflarının karekterizasyonu
verilmiştir.

Anahtar Kelimeler

Hemen hemen yakınsaklık, Genelleştirilmiş ağırlıklı ortalama, Dizi uzayı, Matris Dönüşümleri

Kaynakça

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