Hemen Hemen Yakınsak Dizi Uzaylar için Yeni Bir Bakış

Banach limiti (Acta. Math. 80. 1948, 167-190) kavramını kullanarak G.G. Lorentz hemen hemen yakınsak dizilerin c^ uzayını tanımladı. Bu çalışmada öne çıkan nokta 0 c^ , c^ ve c^s uzaylarının Candan [2] tarafından tanımlanan R G B ~ . ~ = matris etki alanında olan B G c ~ 0^ , B Gc ~ ^ ve B G cs ~ ^ uzaylarını tanımlamaktır. Burada B ~ ikili dizisel band matrisi G de genelleştirilmiş ağırlıklı ortalamayı göstermektedir. Çalışmada öncelikle B G c ~ 0^ , B Gc ~ ^ ve B G cs ~ ^ uzaylarının sırası ile 0 c^ , c^ ve c^s uzaylarına lineer izomorf oldukları gösterildikten sonra B Gc ~ ^ ve B G cs ~ ^ uzaylarının sırası ile ? - ve ? - dualleri elde edilmiştir. Son bölümde de ? verilen herhangi bir dizi uzayı olmak üzere (^ :?) ~ B Gc ve ( ) B Gc ~ ? : ^ matris sınıflarının karekterizasyonu verilmiştir.

A New Outlook for Almost Convergent Sequence Spaces

The point standing out in the present paper is the sequence spaces B G c ~ 0ˆ , B Gc ~ ˆ and B G cs ~ ˆ produced by the domain of the infinite matrix R G B ~ . ~ = , which is defined in the previous study of Candan [2], where the spaces 0 cˆ , cˆ and cˆs, respectively, are as presented by G.G. Lorentz utilizing the issue of the Banach limits (Acta. Math. 80. 1948, 167-190), and B ~ is 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 0 cˆ , cˆ and cˆs, respectively. In addition to these, γ − and β − duals of the spaces B Gc ~ ˆ and B G cs ~ ˆ are given. Beyond them, the classes (ˆ :λ) ~ B Gc and ( ) B Gc ~ λ : ˆ of infinite matrices are characterized, where λ is a given sequence space.

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