Binom ve Dörtlü Band Matrisinin Kompozisyonu ile Türetilmiş Yeni Dizi Uzayları

Öz

Bu çalışmada, Q dörtlü band matrisi olmak üzere, binom ve dörtlü band matrisinin birleşiminden türetilmiş olan b_0^(a,b) (Q), b_c^(a,b) (Q) ve b_∞^(a,b) (Q) dizi uzaylarını oluşturuyoruz. Çalışma dört ana bölüm olarak hazırlandı. İlk bölümde, daha sonra kullanacağımız bazı temel tanım ve eşitlikler verildi. İkinci bölümde, daha önce çeşitli yazarlar tarafından binom matrisinin etki alanı kullanılarak yapılmış çalışmalardan bazılarına ayrıntılı olarak değinildi. Ardından, üç yeni dizi uzayı olan b_0^(a,b) (Q), b_c^(a,b) (Q) ve b_∞^(a,b) (Q) tanımlandı. Daha sonra elde edilen bu dizi uzaylarının BK-uzayı olduğu gösterildi. Bundan sonra b_0^(a,b) (Q), b_c^(a,b) (Q) ve b_∞^(a,b) (Q) dizi uzaylarının sırasıyla c_0, c ve l_∞ dizi uzaylarına lineer olarak izomorf oldukları gösterildi. Ardından bazı içerme bağınları verildi. Üçüncü bölümde elde ettiğimiz yeni dizi uzaylarından b_0^(a,b) (Q) ve b_c^(a,b) (Q) nin Schauder bazları verildi ve b_0^(a,b) (Q), b_c^(a,b) (Q) ve b_∞^(a,b) (Q) dizi uzaylarının α-, β- ve γ- dualleri belirlendi. Dördüncü bölümde bazı matris sınıflarını karakterize edildi. Sonuç olarak binom ve dörtlü band matrisinin birleşiminden elde edilen yeni matrisin daha önce elde edilenlerden daha genel ve kapsamlı sonuçlar verdiği görüldü.

Anahtar Kelimeler

• Matris dönüşümleri
• Matris etki alanı
• Schauder bazı
• α- β- ve γ- dualleri
• Matris sınıfları

New Sequence Spaces Derived by the Composition of Binomial and Quadruple Band Matrices

Öz

In this work, we construct the sequence spaces b_0^(a,b) (Q), b_c^(a,b) (Q) and b_∞^(a,b) (Q), derived from the combination of binomial and quadruple band matrices, where Q is a quadruple band matrix. The study is divided into four main sections. The first section provides some fundamental definitions and equations that will be used later. In the second section, detailed discussions are made on some works previously completed by various authors using the domain of the binomial matrix. Then, the three new sequence spaces b_0^(a,b) (Q), b_c^(a,b) (Q) and b_∞^(a,b) (Q) are defined. It is then shown that these obtained sequence spaces are BK-spaces. Following this, it is demonstrated that b_0^(a,b) (Q), b_c^(a,b) (Q) and b_∞^(a,b) (Q) sequence spaces are linearly isomorphic to the spaces c_0, c and l_∞, in turn, followed by some inclusion relations. In the third section, the Schauder bases of the new sequence spaces b_0^(a,b) (Q) and b_c^(a,b) (Q) are provided, and the α-, β- and γ- duals of b_0^(a,b) (Q), b_c^(a,b) (Q) and b_∞^(a,b) (Q) sequence spaces are determined. The fourth section characterizes some matrix classes. As a result, it is observed that the new matrix obtained from the combination of binomial and quadruple band matrices provides more general and comprehensive results than those obtained previously.

Anahtar Kelimeler

• Matrix transformations
• Matrix domain
• Schauder basis
• α- β- and γ- duals
• Matrix classes

Kaynakça

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