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

Abstract

AbstractIn this paper, we establish a novel category of sequence spaces $\ell _{p}^{q_{\lambda}}$ ℓ p q λ and $\ell _{\infty}^{q_{\lambda}}$ ℓ ∞ q λ by utlizing q-analogue $\Lambda^{q}$ Λ 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 $\ell _{p}$ ℓ p and $\ell _{\infty}$ ℓ ∞ . Moreover, we obtain the α-, β-, and γ-duals of these sequence spaces. We further characterize the class $(\ell _{p}^{q_{\lambda}},X)$ ( ℓ p q λ , X ) of matrices, where X is any of the spaces $\ell _{\infty }$ ℓ ∞ , c, or $c_{0}$ c 0 . Lastly, our study delves into the exploration of specific geometric properties exhibited by the space $\ell _{p}^{q_{\lambda}}$ ℓ p q λ .