In 1977, Jacob defines Gα, for any 0 ≤ α <∞, as the set of all complex sequences x such that limsup|xk|1/k ≤ α. In this paper, we apply Gu −Gv matrix transformation on the sequences of operators given in the famous Walsh’s equiconvergence theorem, where we have that the difference of two sequences of operators converges to zero in a disk. We show that the Gu −Gv matrix transformation of the dif...

We first recall some properties of infinite tridiagonal matrices considered as matrix transformations in sequence spaces of the forms sξ , sξ , s (c) ξ , or lp(ξ). Then, we give some results on the finite section method for approximating a solution of an infinite linear system. Finally, using a quasi-Newton method, we construct a sequence that converges fast to a solution of an infinite linear ...

Matrices with the structures of Toeplitz, Hankel, Vandermonde and Cauchy types are omnipresent in modern computations in Sciences, Engineering and Signal and Image Processing. The four matrix classes have distinct features, but in [P90] we showed that Vandermonde and Hankel multipliers transform all these structures into each other and proposed to employ this property in order to extend any suc...

Let Sn(F) be the vector space of n × n symmetric matrices over a field F (with certain restrictions on cardinality and characteristic). The transformations φ on the space which satisfy one of the following conditions: 1. det(A+ λB) = det(φ(A) + λφ(B)) for all A,B ∈ Sn(F) and λ ∈ F; 2. φ is surjective and det(A+ λB) = det(φ(A) + λφ(B)) for all A,B and two specific λ; 3. φ is additive and preserv...

Sequence transformations are extrapolation methods. They are used for the purpose of convergence acceleration. In the scalar case, such algorithms can be obtained by two diierent approaches which are equivalent. The rst one is an elimination approach based on the solution of a system of linear equations and it makes use of determinants. The second approach is based on the notion of annihilation...

In this paper, we are interested in the study of operators represented by infinite matrices. Note that in [1], Altay and Başar gave some results on the fine spectrum of the difference operator Δ acting on the sequence spaces c0 and c. Then they dealt with the fine spectrum of the operator B(r,s) defined by a matrix band over the sequence spaces c0 and c. In de Malafosse [3, 5], there are result...

In this paper we extend some of our recent results given in [15], so we consider a matrix transformation A = (ank)n,k≥1 and say that a sequence X = (xn)n≥1 is A-statistically convergent to L ∈ V with respect to the intuitionistic fuzzy normed space (IFNS) V if lim n→∞ 1 n |{k ≤ n : ν ([AX]k − L, t) ≥ ε or 1− μ ([AX]k − L, t) ≥ ε}| = 0 for any ε > 0. The aim of this paper is to give conditions o...

The most general linear operator to transform from new sequence space into another sequence space is actually given by an infinite matrix. In the present paper we represent some sequence spaces and give the characterization of (S (p), ) and (S (p), ).

Let w, γ, γo, c, co and l∞ be the spaces of all, summable, summable to zero, convergent, null and bounded sequences respectively. The notion of statistical convergence of sequences was introduced by Fast [3], Schoenberg [12] and Buck [1] independently. Later on the idea was exploited from sequence space point of view and linked with summability by Fridy [4], S̆alát [11], Kolk [5], Rath and Tripa...

The Lewenstein-Sanpera decomposition for a generic two-qubit density matrix is obtained by using Wootters’s basis. It is shown that the average concurrence of the decomposition is equal to the concurrence of the state. It is also shown that all the entanglement content of the state is concentrated in the Wootters’s state |x1〉 associated with the largest eigenvalue λ1 of the Hermitian matrix √√ ...