scholarly journals A decomposition of En (n≥3) into points and a null sequence of cellular sets

1979 ◽  
Vol 10 (3) ◽  
pp. 297-304 ◽  
Author(s):  
David G. Wright
Keyword(s):  
Null Sequence

scholarly journals NOTES ON GRAPH-CONVERGENCE FOR MAXIMAL MONOTONE OPERATORS

2010 ◽  
Vol 83 (1) ◽  
pp. 22-29 ◽  
Author(s):  
FILOMENA CIANCIARUSO ◽  
GIUSEPPE MARINO ◽  
LUIGI MUGLIA ◽  
HONG-KUN XU
Keyword(s):  
Monotone Operator ◽  
Maximal Monotone Operator ◽  
Maximal Monotone ◽  
Maximal Monotone Operators ◽  
Monotone Operators ◽  
Null Sequence ◽  
Graph Convergence ◽  
Common Domain

AbstractWe construct a sequence {An} of maximal monotone operators with a common domain and converging, uniformly on bounded subsets, to another maximal monotone operator A; however, the sequence {t−1nAn} fails to graph-converge for some null sequence {tn}.

scholarly journals Nilsequences and multiple correlations along subsequences

2018 ◽  
Vol 40 (6) ◽  
pp. 1634-1654 ◽  
Author(s):  
ANH NGOC LE
Keyword(s):  
Continuous Function ◽  
Ergodic Average ◽  
Null Sequence

The results of Bergelson, Host and Kra, and Leibman state that a multiple polynomial correlation sequence can be decomposed into a sum of a nilsequence (a sequence defined by evaluating a continuous function along an orbit in a nilsystem) and a null sequence (a sequence that goes to zero in density). We refine their results by proving that the null sequence goes to zero in density along polynomials evaluated at primes and along the Hardy sequence $(\lfloor n^{c}\rfloor )$. In contrast, given a rigid sequence, we construct an example of a correlation whose null sequence does not go to zero in density along that rigid sequence. As a corollary of a lemma in the proof, the formula for the pointwise ergodic average along polynomials of primes in a nilsystem is also obtained.

scholarly journals Some New Type Sigma Convergent Sequence Spaces and Some New Inequalities

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Kuddusi Kayaduman ◽  
Mehmet Şengönül
Keyword(s):  
Convergent Sequence ◽  
Sequence Spaces ◽  
Null Sequence ◽  
New Type ◽  
New Inequalities

We have discussed some important problems about the spacesV~σandV~0σof Cesàro sigma convergent and Cesàro null sequence.

Lobb's generalisation of Catalan's parenthesisation problem revisited

2012 ◽  
Vol 96 (535) ◽  
pp. 56-65
Author(s):  
Thomas Koshy
Keyword(s):  
Null Sequence ◽  
Left And Right

In 1838, the Belgian mathematician Eugene C. Catalan (1814-1894) discovered that the number Cn of well-fonned sequences, with n pairs of left and right parentheses, is given by where n > 0 [1, 2]. For example, there are exactly five well-formed sequences with three pairs of left and right parentheses: ()()(), ()(()), (())(), (()()), ((())). The case n = 0 yields the null sequence, often denoted by λ. Notice that ()) and ((()()), for example, are not correctly parenthesised.

scholarly journals Remarks on the range of a vector measure

1994 ◽  
Vol 36 (2) ◽  
pp. 157-161 ◽  
Author(s):  
Jesús M. F. Castilo ◽  
Fernando Sánchez
Keyword(s):  
Vector Measure ◽  
Null Sequence ◽  
Property A ◽  
Weakly Compact ◽  
Countably Additive Vector Measure ◽  
Additive Vector ◽  
Standing Problem ◽  
Additive Vector Measure

A long-standing problem is the characterization of subsets of the range of a vector measure. It is known that the range of a countably additive vector measure is relatively weakly compact and, in addition, possesses several interesting properties (see [2]). In [6] it is proved that if m: Σ → Χ is a countably additive vector measure, then the range of m has not only the Banach–Saks property, but even the alternate Banach-Saks property. A tantalizing conjecture, which we shall disprove in this article, is that the range of m has to have, for some p > 1, the p-Banach–Saks property. Another conjecture, which has been around for some time (see [2]) and is also disproved in this paper, is that weakly null sequences in the range of a vector measure admit weakly-2-summable sub-sequences. In fact, we shall show a weakly null sequence in the range of a countably additive vector measure having, for every p < ∞, no weakly-p-summable sub-sequences.

Inclusion of sets of regular summability matrices

1964 ◽  
Vol 60 (4) ◽  
pp. 705-712 ◽  
Author(s):  
J. W. Baker ◽  
G. M. Petersen
Keyword(s):  
Finite Subset ◽  
Null Sequence ◽  
Fixed Sequence ◽  
Summable Sequence ◽  
The Matrix ◽  
Summability Matrices ◽  
Image Position ◽  
Regular Summability ◽  
Bounded Sequences

1. In this paper we wish to discuss some problems which arise from a paper by Lorentz and Zeller; see (5). If {μn} is a fixed sequence monotonically increasing to infinity, and every sequence {sn} summed by both of the regular matrices A = (amn) and B = (bmn) and satisfying sn = O{μn) is summed to the same value by both matrices, the matrices are called (μn)-consistent. The two matrices are called consistent if they are (μn)-consistent for all {μn}, μn↗∞; they are b-consistent if the bounded sequences summed by both are summed to the same value by both. The matrix A is said to be (μn)-stronger than the matrix B, if every sequence {μn} that is B summable and satisfying sn = O(μn) is also A summable. The matrix A is stronger than B if every B summable sequence is A summable; A is b-stronger if every bounded B summable sequence is A summable. The symbol A -lim x denotes the value to which the sequence x = {xn} is summed by A; Am(x) is the transformationand A(x) is the sequence {Am(x)}. Let {A(i)}i ∈ I be any family, infinite or finite, of regular summability matrices. This family is called simultaneously consistent if, given any finite subset of I, say F, and any set of sequences {x(i)i ∈ F such that A(i) sums x(i) for each i in F, and such that is the null sequence, then .

scholarly journals Homotopy and the Kestelman–Borwein–Ditor Theorem

2011 ◽  
Vol 54 (1) ◽  
pp. 12-20 ◽  
Author(s):  
N. H. Bingham ◽  
A. J. Ostaszewski
Keyword(s):  
Functional Form ◽  
Null Sequence ◽  
Unified Approach ◽  
Large Sets ◽  
Functional Version

AbstractThe Kestelman–Borwein–Ditor Theorem, on embedding a null sequence by translation in (measure/category) “large” sets has two generalizations. Miller replaces the translated sequence by a “sequence homotopic to the identity”. The authors, in a previous paper, replace points by functions: a uniform functional null sequence replaces the null sequence, and translation receives a functional form. We give a unified approach to results of this kind. In particular, we show that (i) Miller's homotopy version follows fromthe functional version, and (ii) the pointwise instance of the functional version follows from Miller's homotopy version.

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