On composition operators of Fibonacci matrix and applications of Hausdorff measure of noncompactness

The aim of the paper is introduced the composition of the two infinite matrices $\Lambda=(\lambda_{nk})$ and $\widehat{F}=\left( f_{nk} \right).$ Further, we determine the $\alpha$-, $\beta$-, $\gamma$-duals of new spaces and also construct the basis for the space $\ell_{p}^{\lambda}(\widehat{F}).$ Additionally, we characterize some matrix classes on the spaces $\ell_{\infty}^{\lambda}(\widehat{F})$ and $\ell_{p}^{\lambda}(\widehat{F}).$ We also investigate some geometric properties concerning Banach-Saks type $p.$Finally we characterize the subclasses $\mathcal{K}(X:Y)$ of compact operators by applying the Hausdorff measure of noncompactness, where $X\in\{\ell_{\infty}^{\lambda}(\widehat{F}),\ell_{p}^{\lambda}(\widehat{F})\}$ and $Y\in\{c_{0},c, \ell_{\infty}, \ell_{1}, bv\},$ and $1\leq p<\infty.$

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.

Poisson like matrix operator and its application in p-summable space

The incomplete gamma function Γ(a, u) is defined by Γ ( a , u ) = ∫ u ∞ t a − 1 e − t d t , $$\Gamma(a,u)=\int\limits_{u}^{\infty}t^{a-1}\textrm{e}^{-t}\textrm{d} t,$$ where u > 0. Using the incomplete gamma function, we define a new Poisson like regular matrix P ( μ ) = ( p n k μ ) $\mathfrak{P}(\mu)=(p^{\mu}_{nk})$ given by p n k μ = n ! Γ ( n + 1 , μ ) e − μ μ k k ! ( 0 ≤ k ≤ n ) , 0 ( k > n ) , $$p^{\mu}_{nk}= \begin{cases} \dfrac{n!}{\Gamma(n+1,\mu)}\dfrac{\textrm{e}^{-\mu}\mu^k}{k!} \quad &(0\leq k\leq n), \\[1ex] 0\quad & (k>n), \end{cases}$$ where μ > 0 is fixed. We introduce the sequence space ℓ p ( P ( μ ) ) $\ell_p(\mathfrak{P}(\mu))$ for 1 ≤ p ≤ ∞ and some topological properties, inclusion relations and generalized duals of the newly defined space are discussed. Also we characterize certain matrix classes and compact operators related to the space ℓ p ( P ( μ ) ) $\ell_p(\mathfrak{P}(\mu))$ . We obtain Gurarii’s modulus of convexity and investigate some geometric properties of the new space. Finally, spectrum of the operator P ( μ ) $\mathfrak{P}(\mu)$ on sequence space c 0 has been investigated.

Characterization of Matrix Classes Transforming Between Almost Sure Convergent Sequences of Complex Uncertain Variables

The study of uncertainty theory evolved and developed largely in the last decade. In this paper, we introduce the concept of summability and absolutely summability with respect to almost surely through matrix transformation of complex uncertain sequences and establish the interrelationship between these two concepts. In this context, applications of matrix transformation of complex uncertain sequences are also presented.

A class of symmetric and non-symmetric band matrices via binomial coefficients

Symmetric matrix classes of bandwidth 2r + 1 was studied in 1972 through binomial coefficients. In this paper, non-symmetric matrix classes with the binomial coefficients are considered where r + s + 1 is the bandwidth, r is the lower bandwidth and s is the upper bandwidth. Main results for inverse, determinants and norm-infinity of inverse are presented. The binomial coefficients are used for the derivation of results.

Almost convergent sequence spaces derived by the domain of quadruple band matrix

In this work, we construct the sequence spaces f(Q(r, s, t, u)), f0(Q(r, s, t, u)) and fs(Q(r, s, t, u)), where Q(r, s, t, u) is quadruple band matrix which generalizes the matrices Δ3, B(r, s, t), Δ2, B(r, s) and Δ, where Δ3, B(r, s, t), Δ2, B(r, s) and Δ are called third order difference, triple band, second order difference, double band and difference matrix, respectively. Also, we prove that these spaces are BK-spaces and are linearly isomorphic to the sequence spaces f, f0 and fs, respectively. Moreover, we give the Schauder basis and β, γ-duals of those spaces. Lastly, we characterize some matrix classes related to those spaces.

On sequence spaces defined by the domain of a regular tribonacci matrix

In this article we introduce Tribonacci sequence spaces ℓp(T) (1 ≤ p ≤ ∞) derived by the domain of a newly defined regular Tribonacci matrix. We give some topological properties, inclusion relation, obtain the Schauder basis and determine the α-, β- and γ-duals of the new spaces. We characterize the matrix classes on ℓp(T). Finally, we give some geometric properties of the space ℓp(T).