Characterization of a New Type of Topological Sequence Spaces and Some Properties

Abstract

Examination of spaces in the field of functional analysis, especially revealing their topological and algebraic structures, is very important in terms of forming a basis for studies in the field of pure mathematics and applied sciences. In this context, topology, which was widely used only in the field of geometry at the beginning, gave a solid foundation to the fields in which it was used by causing methodological changes in all branches of mathematics over time. Frechet-Coordinate space (FK space) is a concept that has a functional role in fields such as topological sequence spaces and summability. Topological vector spaces are described as linear spaces defined by a topology that provides continuous vector space operations. If this vector space has a complete metric space structure, it is called Frechet space, and if it has a topology with continuous coordinate functions, it is called Frechet-Coordinate (FK) space. The theory of FK spaces has gained more importance in recent years and has found applications in various fields thanks to the efforts of many researchers. If the topology of an FK space can be derived from the norm, this space is called as a BK space. In this study, cs_0^λ (Δ), cs^λ (Δ), and bs^λ (Δ) difference sequence spaces are defined, and it is revealed that these spaces are BK spaces. In addition, considering the topological properties of these spaces, some spaces that are isomorphic and their duals have been determined.

Keywords

• BK spaces
• Difference sequence spaces
• Frechet-coordinate spaces
• Schauder basis
• Topological sequence spaces

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