Some Topological and Geometric Properties of Some New Spaces ofλ-Convergent and Bounded Series

Abstract

The main purpose of this study is to introduce the spacescsλ,cs0λ, andbsλwhich areBK-spaces of nonabsolute type. We prove that these spaces are linearly isomorphic to the spacescs,cs0, andbs, respectively, and derive some inclusion relations. Additionally, Schauder bases of the spacescsλandcs0λhave been constructed and theα-,β-, andγ-duals of these spaces have been computed. Besides, we characterize some matrix classes from the spacescsλ,cs0λ, andbsλto the spaceslp,c, andc0, 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.