Infinite Matrices and Sequence Spaces

1951 ◽  
Vol 35 (314) ◽  
pp. 277
Author(s):  
P. Vermes ◽  
Richard G. Cooke
Keyword(s):  
Sequence Spaces ◽  
Infinite Matrices

scholarly journals Fine Spectra of Tridiagonal Symmetric Matrices

2011 ◽  
Vol 2011 ◽  
pp. 1-10 ◽  
Author(s):  
Muhammed Altun
Keyword(s):  
Explicit Form ◽  
Resolvent Operator ◽  
Sequence Spaces ◽  
Symmetric Matrices ◽  
Infinite Matrices ◽  
Banded Matrices ◽  
Lower Triangular ◽  
The Resolvent Operator

The fine spectra of upper and lower triangular banded matrices were examined by several authors. Here we determine the fine spectra of tridiagonal symmetric infinite matrices and also give the explicit form of the resolvent operator for the sequence spaces , , , and .

scholarly journals The αAB-, βAB-, γab- and NAB-duals for sequence spaces

Filomat ◽  
2017 ◽  
Vol 31 (19) ◽  
pp. 6219-6231
Author(s):  
D. Foroutannia ◽  
H. Roopaei
Keyword(s):  
Sequence Spaces ◽  
The Other ◽  
Infinite Matrices ◽  
Multiplier Space

Let A = (an,k) and B = (bn,k) be two infinite matrices with real entries. The main purpose of this paper is to generalize the multiplier space for introducing the concepts of ?AB-, ?AB-, ?AB-duals and NAB-duals. Moreover, these duals are investigated for the sequence spaces X and X(A), where X ? {c0, c, lp} for 1 ? p ? ?. The other purpose of the present study is to introduce the sequence spaces X(A,?) = {x=(xk): (?x?k=1 an,kXk - ?x?k=1 an-1,kXk)? n=1 ? X}, where X ? {l1,c,c0}, and computing the NAB-(or Null) duals and ?AB-duals for these spaces.

scholarly journals Matrix Transformations between Certain Sequence Spaces over the Non-Newtonian Complex Field

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Uğur Kadak ◽  
Hakan Efe
Keyword(s):  
Linear Operator ◽  
Sufficient Conditions ◽  
Sequence Spaces ◽  
General Linear ◽  
Matrix Transformations ◽  
Infinite Matrix ◽  
Complex Field ◽  
Infinite Matrices ◽  
The Matrix ◽  
Necessary And Sufficient

In some cases, the most general linear operator between two sequence spaces is given by an infinite matrix. So the theory of matrix transformations has always been of great interest in the study of sequence spaces. In the present paper, we introduce the matrix transformations in sequence spaces over the fieldC*and characterize some classes of infinite matrices with respect to the non-Newtonian calculus. Also we give the necessary and sufficient conditions on an infinite matrix transforming one of the classical sets overC*to another one. Furthermore, the concept for sequence-to-sequence and series-to-series methods of summability is given with some illustrated examples.

scholarly journals Some new sequence spaces and almost convergence

Filomat ◽  
2008 ◽  
Vol 22 (2) ◽  
pp. 59-64 ◽  
Author(s):  
Sameer Gupkari
Keyword(s):  
Sequence Space ◽  
Sequence Spaces ◽  
Almost Convergence ◽  
Infinite Matrices

The sequence space arc have been defined and the classes (arc : lp) and (arc : c) of infinite matrices have been characterized by Aydin and Ba?ar (On the new sequence spaces which include the spaces c0 and c, Hokkaido Math. J. 33(2) (2004), 383-398) [1], where 1 ? p ? ?. The main purpose of the present paper is to characterize the classes (arc : f) and (arc : f0), where f and f0 denote the spaces of almost convergent and almost convergent null sequences with real or complex terms. .

scholarly journals New approach to some results related to mixed norm sequence spaces

Filomat ◽  
2016 ◽  
Vol 30 (1) ◽  
pp. 83-88 ◽  
Author(s):  
Ivana Djolovic ◽  
Eberhard Malkowsky ◽  
Katarina Petkovic
Keyword(s):  
Hausdorff Measure ◽  
Measure Of Noncompactness ◽  
Diagonal Matrix ◽  
Sequence Spaces ◽  
Mixed Norm ◽  
Hausdorff Measure Of Noncompactness ◽  
Infinite Matrices ◽  
New Approach ◽  
The Subject ◽  
Bk Spaces

In this paper, the mixed norm sequence spaces ?p,q for 1 ? p,q ? ? are the subject of our research; we establish conditions for an operator T? to be compact, where T? is given by a diagonal matrix. This will be achieved by applying the Hausdorff measure of noncompactness and the theory of BK spaces. This problem was treated and solved in [5, 6], but in a different way, without the application of the theory of infinite matrices and BK spaces. Here, we will present a new approach to the problem. Some of our results are known and others are new.

SOME ALMOST CONVERGENT SEQUENCE SPACES OF FUZZY NUMBERS GENERATED BY INFINITE MATRICES

2006 ◽  
Vol 02 (02) ◽  
pp. 115-121
Author(s):  
EKREM SAVAS
Keyword(s):  
Fuzzy Numbers ◽  
Convergent Sequence ◽  
Sequence Spaces ◽  
Topological Properties ◽  
Infinite Matrices ◽  
Almost Convergent Sequence ◽  
Inclusion Relations

In this paper we define some almost convergent sequence spaces of fuzzy numbers by using the A-transforms and we also examine topological properties and some inclusion relations for these new sequence spaces.

scholarly journals Vector-valued sequence spaces generated by infinite matrices

2001 ◽  
Vol 26 (9) ◽  
pp. 547-560
Author(s):  
Nandita Rath
Keyword(s):  
Sequence Spaces ◽  
Infinite Matrix ◽  
Real Sequence ◽  
Normed Spaces ◽  
Infinite Matrices ◽  
Positive Real ◽  
The Matrix ◽  
Almost All ◽  
Vector Valued

LetA=(ank)be an infinite matrix with allank≥0andPa bounded, positive real sequence. For normed spacesEandEkthe matrixAgenerates paranormed sequence spaces such as[A,P]∞((Ek)),[A,P]0((Ek)), and[A,P](E)which generalize almost all the existing sequence spaces, such asl∞,c0,c,lp,wp, and several others. In this paper, conditions under which these three paranormed spaces are separable, complete, andr-convex, are established.

Paranormed sequence spaces generated by infinite matrices

1968 ◽  
Vol 64 (2) ◽  
pp. 335-340 ◽  
Author(s):  
I. J. Maddox
Keyword(s):  
Linear Space ◽  
Sequence Spaces ◽  
Topological Linear Space ◽  
Infinite Matrices ◽  
Paranormed Space ◽  
Complex Sequences ◽  
Complex Linear ◽  
Topological Linear ◽  
Subadditive Function

A paranormed space X = (X, g) is a topological linear space in which the topology is given by paranorm g—a real subadditive function on X such that g(θ) = 0, g(x) = g(−x) and such that multiplication is continuous. In the above, θ is the zero in the complex linear space X and continuity of multiplication means that λn → λ, xn → x(i.e. g(xn − x) → 0) imply λnxn → λx, for scalars λ and vectors x. We shall use the term semimetric function to describe a real subadditive function g on X such that g(θ) = 0, g(x) = g(−x). Two familiar paranormed sequence spaces, which have been extensively studied (3), are l(p) and m(p). For a given sequence p = (gk) of strictly positive numbers, l;(p) is the set of all complex sequences x = (xk) such that and m(p) is the set of x such that sup Throughout, sums and suprema without limits are taken from 1 to ∞. Simons (3) considered only the case in which 0 < pk ≤ 1 so that natural paranorms would seem to be in m(p). In fact Simons showed that g1 was a paranorm for l(p), but that g2 did not satisfy the continuity of multiplication axiom.

Infinite matrices and Cesàro sequence spaces

1997 ◽  
Vol 23 (1) ◽  
pp. 3-11 ◽  
Author(s):  
F. M. Khan ◽  
M. F. Rahman ◽  
Ф. М. Хан ◽  
М. Ф. Рахман
Keyword(s):  
Sequence Spaces ◽  
Infinite Matrices
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