Subdivisions of the spectra for D(r,0,s,0,t) operator on certain sequence spaces

In this paper we have examined the approximate point spectrum, defect spectrum and compression spectrum of the operator D(r,0,s,0,t) on the sequence spaces c0, c, and $bv_p (1<p<\infty)$.

A Study of Fuzzy Sequence Spaces

The purpose of this chapter is to introduce and study some new ideal convergence sequence spaces FSJθT, FS0JθT and FS∞JθT on a fuzzy real number F defined by a compact operator T. We investigate algebraic properties like linearity, solidness and monotinicity with some important examples. Further, we also analyze closedness of the subspace and inclusion relations on the said spaces.

On The Quadruple Sequence Spaces of Fuzzy Complex Numbers

In this paper, the quadruple sequence spaces of fuzzy complex numbers are shown, and several features such as solidity, symmetry, monotonicity, and convergence-free are discussed.

Some classes of sequence spaces defined by a Musielak-Orlicz function

In the present paper we introduce the sequence spaces c0{ℳ, Λ , p, q}, c{ℳ, Λ, p, q} and l ∞ {ℳ, Λ, p, q} defined by a Musielak-Orlicz function ℳ = (ℳk). We study some topological properties and prove some inclusion relations between these spaces.

On inclusion properties of discrete Morrey spaces

We discuss a necessary condition for inclusion relations of weak type discrete Morrey spaces which can be seen as an extension of the results in [H. Gunawan, E. Kikianty and C. Schwanke, Discrete Morrey spaces and their inclusion properties, Math. Nachr. 291 2018, 8–9, 1283–1296] and [D. D. Haroske and L. Skrzypczak, Morrey sequence spaces: Pitt’s theorem and compact embeddings, Constr. Approx. 51 2020, 3, 505–535]. We also prove a proper inclusion from weak type discrete Morrey spaces into discrete Morrey spaces. In addition, we give a necessary condition for this inclusion. Some connections between the inclusion properties of discrete Morrey spaces and those of Morrey spaces are also discussed.

Compact operators on sequence spaces associated with the Copson matrix of order α

In this work, we study characterizations of some matrix classes $(\mathcal{C}^{(\alpha )}(\ell ^{p}),\ell ^{\infty })$ ( C ( α ) ( ℓ p ) , ℓ ∞ ) , $(\mathcal{C}^{(\alpha )}(\ell ^{p}),c)$ ( C ( α ) ( ℓ p ) , c ) , and $(\mathcal{C}^{(\alpha )}(\ell ^{p}),c^{0})$ ( C ( α ) ( ℓ p ) , c 0 ) , where $\mathcal{C}^{(\alpha )}(\ell ^{p})$ C ( α ) ( ℓ p ) is the domain of Copson matrix of order α in the space $\ell ^{p}$ ℓ p ($0< p<1$ 0 < p < 1 ). Further, we apply the Hausdorff measures of noncompactness to characterize compact operators associated with these matrices.