Work

ON THE JORDAN-TYPE SEQUENCE SPACES WHICH INCLUDE THE SPACES c AND $$c_0$$ AND COMPACT OPERATORS

Year: 2026

Type: article

Abstract: In this study, novel sequence spaces are introduced as the domains of the Jordan-type matrix operator within the spaces of c and $$c_0$$ c 0 . Initially, these new spaces are defined, and their fundamental properties, including completeness and other topological characteristics, are examined. Furthermore, the existence of a Schauder basis for these spaces is established, highlighting its crucial role in their structural analysis. Next, the $$\alpha $$ α -, $$\beta $$ β -, and $$\gamma $$ γ -duals of the newly constructed sequence spaces are determined to provide a deeper understanding of their duality relations. Subsequently, the classes of infinite matrices that map sequences from these new spaces into classical sequence spaces, such as $$\ell _p$$ ℓ p , $$\ell _{\infty }$$ ℓ ∞ , c , and $$c_0$$ c 0 , are characterized, along with the reverse transformations. Finally, attention is given to compact operators acting on these spaces, and a comprehensive characterization of their behavior is provided. Necessary and sufficient conditions for compactness are explored, and their implications in functional analysis are discussed.

Source: Journal of Mathematical Sciences

DOI: 10.1007/s10958-026-08432-0

Authors: Hacer Bilgin Ellidokuzoğlu, Sezer Erdem, Serkan Demiriz, Merve İlkhan Kara

Institutions: Recep Tayyip Erdoğan University, Malatya Turgut Özal Üniversitesi, Turgut Özal University, Tokat Gaziosmanpaşa Üniversitesi, Düzce Üniversitesi

Language: English

Topic: Approximation Theory and Sequence Spaces

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,490

Funder: Recep Tayyip Erdogan Üniversitesi