Submatrices of summability matrices
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In this paper, it was shown that a matrix that maps l 1 into l 1 can be obtained from any regular matrix by the deletion of rows from a matrix preserving boundedness.Abstract:
It is proved that a matrix that maps l1 into l1 can be obtained from any regular matrix by the deletion of rows. Similarly, a conservative matrix can be obtained by deletion of rows from a matrix that preserves boundedness. These techniques are also used to derive a simple sufficient condition for a matrix to sum an unbounded sequence.read more
Citations
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On statistical convergence and statistical monotonicity
TL;DR: In this article, the authors investigate properties of statistically convergent sequences and introduce the denition of statistical mono- tonicity and upper (or lower) peak points of real valued sequences.
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Inclusion results for convolution submethods
Jeffrey A. Osikiewicz,M. K. Khan +1 more
TL;DR: If B is a summability matrix, then the submethod Bλ is the matrix obtained by deleting a set of rows from the matrix B, and an equivalence result for convolution submethods is established.
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Analogues of some Tauberian theorems for bounded variation
TL;DR: In this article, the notion of bounded variation and the concept of regularity for four-dimensional matrices were introduced and the following two questions were answered: 1) If there exists a four dimensional regular matrix A such that Ay = Σ k,l=1,1 ∞∞ ∞ a m,n,k,l y k, l is of bounded variations for every subsequence y of x, does it necessarily follow that x ∈ BV?
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Submatrices of Four Dimensional Summability Matrices
TL;DR: In this paper, it was shown that a matrix that maps l ∆ into l ∀ can be obtained from any RH-regular matrix by the deletion of rows, and that a four dimensional conservative matrix can also be obtained by the removal of rows from a matrix preserving boundedness.
References
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Journal Article
A new class of sequence spaces with applications in summability theory.
TL;DR: In this paper, the authors study topological sequence spaces in which the coordinate vectors converge to zero and give characterizations of these spaces, based on the Köthe-Toeplitz theory of solid sequence spaces.
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A simple sufficient condition that a method of summability be stronger than convergence
TL;DR: Toeplitz [l91l] proved that A is regular if and only if the three conditions (i.e., a sequence sn is summable A, sn exists and sn belongs to the summability field of A) are satisfied.
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A note on absolute summability
TL;DR: For real inner product spaces X we may also reduce the proof of the corresponding theorem to showing that a certain quadratic equation with real coefficients has real roots as mentioned in this paper, which proves slightly more than what we set out to prove.
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Absolute summability matrices that are stronger than the identity mapping
TL;DR: The main result of as discussed by the authors is that the matrix A maps 1A properly into 11, i.e., 11 ; A-1[11], and that the means of Norlund, Euler-Knopp, Taylor, and Hausdorff are investiga.
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