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

Kübra Topal

Article Details

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

Authors:

Kübra Topal

Publisher:

Recep Tayyip Erdoğan University

Main Topics:

Operatör Cebirleri ve Fonksiyonel Analiz

Journal:

Recep Tayyip Erdoğan Üniversitesi Fen ve Mühendislik Bilimleri Dergisi Vol.5 Issue 2, pp.76-92

Document Type:

Article

Publication Date:

12/2024

Document Language:

English

Document ID (Org No.):

2001337953

pISSN:

2687-2315

Keywords:

Abstract:

 In this work, we construct the sequence spaces b_0a,b Q, b_ca,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_0a,b Q, b_ca,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_0a,b Q, b_ca,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_0a,b Q and b_ca,b Q are provided, and the α-, β- and γ- duals of b_0a,b Q, b_ca,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.

 In this work, we construct the sequence spaces b_0a,b Q, b_ca,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_0a,b Q, b_ca,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_0a,b Q, b_ca,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_0a,b Q and b_ca,b Q are provided, and the α-, β- and γ- duals of b_0a,b Q, b_ca,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.

 In this work, we construct the sequence spaces b_0a,b Q, b_ca,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_0a,b Q, b_ca,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_0a,b Q, b_ca,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_0a,b Q and b_ca,b Q are provided, and the α-, β- and γ- duals of b_0a,b Q, b_ca,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.

 Bu çalışmada, Q dörtlü band matrisi olmak üzere, binom ve dörtlü band matrisinin birleşiminden türetilmiş olan b_0a,b Q, b_ca,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_0a,b Q, b_ca,b Q ve b_a,b Q tanımlandı. Daha sonra elde edilen bu dizi uzaylarının BK-uzayı olduğu gösterildi. Bundan sonra b_0a,b Q, b_ca,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_0a,b Q ve b_ca,b Q nin Schauder bazları verildi ve b_0a,b Q, b_ca,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.

Article Details

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

Authors:

Kübra Topal

Publisher:

Recep Tayyip Erdoğan University

Main Topics:

Operatör Cebirleri ve Fonksiyonel Analiz

Journal:

Recep Tayyip Erdoğan Üniversitesi Fen ve Mühendislik Bilimleri Dergisi Vol.5 Issue 2, pp.76-92

Document Type:

Article

Publication Date:

12/2024

Document Language:

English

Document ID (Org No.):

2001337953

pISSN:

2687-2315

Matrix transformations

Matrix domain

Schauder basis

α- β- and γ- duals

Matrix classesMatris dönüşümleri

Matris etki alanı

Schauder bazı

α- β- ve γ- dualleri

Matris sınıfları

Issues

Article Details

Authors: Kübra Topal

Publisher: Recep Tayyip Erdoğan University

Main Topics: Operatör Cebirleri ve Fonksiyonel Analiz

Journal: Recep Tayyip Erdoğan Üniversitesi Fen ve Mühendislik Bilimleri Dergisi Vol.5 Issue 2, pp.76-92

Document Type: Article

Publication Date: 12/2024

Document Language: English

Document ID (Org No.): 2001337953

pISSN: 2687-2315

Issues

Authors:

Kübra Topal

Publisher:

Recep Tayyip Erdoğan University

Main Topics:

Operatör Cebirleri ve Fonksiyonel Analiz

Journal:

Recep Tayyip Erdoğan Üniversitesi Fen ve Mühendislik Bilimleri Dergisi Vol.5 Issue 2, pp.76-92

Document Type:

Article

Publication Date:

12/2024

Document Language:

English

Document ID (Org No.):

2001337953

pISSN:

2687-2315