Sequence spaces derived by q λ $q_{\lambda}$ operators in ℓ p $\ell _{p}$ spaces and their geometric properties

Abstract

Abstract In this paper, we establish a novel category of sequence spaces ℓ p q λ $\ell _{p}^{q_{\lambda}}$ and ℓ ∞ q λ $\ell _{\infty}^{q_{\lambda}}$ by utlizing q-analogue Λ q $\Lambda^{q}$ of Λ-matrix. Our investigation outlines several topological characteristics and inclusion results of these newly introduced sequence spaces, specifically identifying them as BK-spaces. Subsequently, we demonstrate that these novel sequence spaces are of nonabsolute type and establish their isometric isomorphism with ℓ p $\ell _{p}$ and ℓ ∞ $\ell _{\infty}$ . Moreover, we obtain the α-, β-, and γ-duals of these sequence spaces. We further characterize the class ( ℓ p q λ , X ) $(\ell _{p}^{q_{\lambda}},X)$ of matrices, where X is any of the spaces ℓ ∞ $\ell _{\infty }$ , c, or c 0 $c_{0}$ . Lastly, our study delves into the exploration of specific geometric properties exhibited by the space ℓ p q λ $\ell _{p}^{q_{\lambda}}$ .

Keywords

• Sequence spaces
• q-Calculus
• q λ $q_{\lambda}$ -Operators
• Duals
• Matrix transformations
• Geometric properties