On the fine spectrum of the upper triangle double band matrix Δ+ on the sequence space c0

In this study, we determine the fine spectrum of the matrix operator ∆+ defined by an upper triangle double band matrix acting on the sequence space c_0 with respect to the Goldberg’s classification. As a new development, we give the approximate point spectrum, defect spectrum and compression spectrum of the matrix operator ∆+ on c_0

On the fine spectrum of triangular triple-band matrix over sequence spaces cc and ellpell_{p},(0<p<1)(0<p<1)

The purpose of this study is to determine the fine spectra of the operator for which the corresponding lower and upper triangular matrices $A(r,s,t)$ and $B(r,s,t)$ are on the sequence spaces $c$ and $ell_{p}$, where $(0<p<1)$, respectively. Further, we obtain the approximate point spectrum, defect spectrum and compression spectrum on these spaces. Furthermore, we give the graphical representations of the spectrum of the triangular triple-band matrix over the sequence spaces $c$ and $ell_{p}$

The Generalized Difference Operator of Order Three and Its Domain in the Sequence Spaces e1 and bv

Most recently, the generalized difference operator Δ3 i of order three was defined and its domain in Hahn sequence space h was calculated. In this paper, the spaces ℓ1(Δ3 i ) and bv(Δ3 i ) are introduced as the domain of generalized difference operator Δ3 i of order three in the sequence spaces ℓ1 and bv. +en, some topological properties of ℓ1(Δ3 i ) and bv(Δ3 i ) are given, and some inclusion relations are shown. Additionally, algebraic dual, α−, β−, and c− dual spaces of ℓ1(Δ3 i ) and bv(Δ3 i ) are computed. In the last section, the classes (μ(Δ3 i ): λ) and (λ: μ(Δ3 i )) of matrix transformations are characterized, where μ � ℓ1 � � , bv and λ � c, c0, ℓ1 � , ℓ∞, bs, cs, bv, h�