Some Topological and Geometric Properties of Some New Spaces of λ-Convergent and Bounded Series. (1st June 2015)

• Record Type: Journal Article
• Authors: Kaya, Meltem; Furkan, Hasan
• Other Names: Fiorenza Alberto Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2015(2015)
• Publication Date: 2015-06-01
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2015/458324
• Languages: English
• ISSNs: 2314-8896

Abstract

Abstract : The main purpose of this study is to introduce the spacesc s λ, c s 0 λ, andb s λ which areB K -spaces of nonabsolute type. We prove that these spaces are linearly isomorphic to the spacesc s, c s 0, andb s, respectively, and derive some inclusion relations. Additionally, Schauder bases of the spacesc s λ andc s 0 λ have been constructed and theα -, β -, andγ -duals of these spaces have been computed. Besides, we characterize some matrix classes from the spacesc s λ, c s 0 λ, andb s λ to the spacesl p, c, andc 0, where1 ≤ p ≤ ∞ . Finally, we examine some geometric properties of these spaces as Gurarǐ's modulus of convexity, propertym ∞, property( M ), property WORTH, nonstrict Opial property, and weak fixed point property.