scholarly journals GROUPOID -ALGEBRAS WITH HAUSDORFF SPECTRUM

2013 ◽  
Vol 88 (2) ◽  
pp. 232-242 ◽  
Author(s):  
GEOFF GOEHLE
Keyword(s):  
Haar System ◽  
Sufficient Conditions ◽  
Orbit Space ◽  
Necessary And Sufficient Conditions ◽  
Locally Compact ◽  
Fell Topology ◽  
Necessary And Sufficient ◽  
Convergent Sequences

AbstractSuppose that $G$ is a second countable, locally compact Hausdorff groupoid with abelian stabiliser subgroups and a Haar system. We provide necessary and sufficient conditions for the groupoid ${C}^{\ast } $-algebra to have Hausdorff spectrum. In particular, we show that the spectrum of ${C}^{\ast } (G)$ is Hausdorff if and only if the stabilisers vary continuously with respect to the Fell topology, the orbit space ${G}^{(0)} / G$ is Hausdorff, and, given convergent sequences ${\chi }_{i} \rightarrow \chi $ and ${\gamma }_{i} \cdot {\chi }_{i} \rightarrow \omega $ in the dual stabiliser groupoid $\widehat{S}$ where the ${\gamma }_{i} \in G$ act via conjugation, if $\chi $ and $\omega $ are elements of the same fibre then $\chi = \omega $.

scholarly journals On the Riesz Almost Convergent Sequences Space

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
Mehmet Şengönül ◽  
Kuddusi Kayaduman
Keyword(s):  
Sequence Space ◽  
Sufficient Conditions ◽  
Riesz Transforms ◽  
Necessary And Sufficient Conditions ◽  
Infinite Matrices ◽  
Necessary And Sufficient ◽  
Convergent Sequences

The purpose of this paper is to introduce new spaces and that consist of all sequences whose Riesz transforms of order one are in the spaces and , respectively. We also show that and are linearly isomorphic to the spaces and , respectively. The and duals of the spaces and are computed. Furthermore, the classes and of infinite matrices are characterized for any given sequence space and determine the necessary and sufficient conditions on a matrix to satisfy , for all .

scholarly journals On the inclusion of a bounded convergence field in the space of almost convergent sequences

1972 ◽  
Vol 13 (1) ◽  
pp. 82-90 ◽  
Author(s):  
Robert E. Atalla
Keyword(s):  
Sufficient Conditions ◽  
Research Problem ◽  
Necessary And Sufficient Conditions ◽  
General Context ◽  
Regular Matrix ◽  
Reverse Inclusion ◽  
Necessary And Sufficient ◽  
Convergent Sequences

Let T = (tmn) be a regular matrix, and CTbe its bounded convergence field. Necessary and sufficient conditions for CT to contain the space of almost convergent sequences are well known. (See, e.g., [7, p.62]). G. M. Petersen has suggested as a problem for research the discovery of necessary and sufficient conditions for the reverse inclusion: When is CT contained in the space of almost convergent sequences? [7, p. 137, research problem 9]. In this paper we deal with this question in a more general context. First we need some notation.

scholarly journals Generalized Nörlund and Nörlund-type Means of Sequences of Fuzzy Numbers

2020 ◽  
Vol 13 (5) ◽  
pp. 1088-1096
Author(s):  
Pradosh Kumar Pattanaik ◽  
Susanta Kumar Paikray ◽  
Bidu Bhusan Jena
Keyword(s):  
Fuzzy Numbers ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Slow Oscillation ◽  
Real Numbers ◽  
Fuzzy Real Numbers ◽  
Sequences Of Fuzzy Numbers ◽  
Necessary And Sufficient ◽  
Convergent Sequences

In this article we study some properties of generalized Nörlund and Nörlund-typemeans of sequences of fuzzy real numbers. We establish necessary and sufficient conditions for our purposed methods to transform convergent sequences of fuzzy real numbers into convergent sequences of fuzzy real numbers which also preserve the limit. Finally, we establish some results showing the connection between the generalized N ̈orlund and N ̈orlund-type limits and the usual limits under slow oscillation of sequences of fuzzy real numbers.

scholarly journals Matrix transformations from absolutely convergent series to convergent sequences as general weighted mean summability methods

2000 ◽  
Vol 24 (8) ◽  
pp. 533-538
Author(s):  
Jinlu Li
Keyword(s):  
Classical Result ◽  
Sufficient Conditions ◽  
Convergent Series ◽  
Necessary And Sufficient Conditions ◽  
Matrix Transformations ◽  
Weighted Mean ◽  
Summability Methods ◽  
Necessary And Sufficient ◽  
Convergent Sequences

We prove the necessary and sufficient conditions for an infinity matrix to be a mapping, from absolutely convergent series to convergent sequences, which is treated as general weighted mean summability methods. The results include a classical result by Hardy and another by Moricz and Rhoades as particular cases.

scholarly journals Measure convergent sequences in Lebesgue spaces and Fatou's lemma

1996 ◽  
Vol 54 (2) ◽  
pp. 197-202 ◽  
Author(s):  
Heinz-Albrecht Klei
Keyword(s):  
Integrable Function ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Uniform Integrability ◽  
Lebesgue Spaces ◽  
Integrable Functions ◽  
Fatou’S Lemma ◽  
Necessary And Sufficient ◽  
Fatou's Lemma ◽  
Convergent Sequences

Let (fn) be a sequence of positive P-integrable functions such that (∫ fndP)n converges. We prove that (fn) converges in measure to if and only if equality holds in the generalised Fatou's lemma. Let f∞ be an integrable function such that (∥fn − f∞∥1)n converges. We present in terms of the modulus of uniform integrability of (fn) necessary and sufficient conditions for (fn) to converge in measure to f∞.

Convolution on L p-spaces of a locally compact group

2013 ◽  
Vol 63 (2) ◽  
Author(s):  
Fatemeh Abtahi ◽  
Rasoul Nasr-Isfahani ◽  
Ali Rejali
Keyword(s):  
Compact Group ◽  
Sufficient Conditions ◽  
Function Spaces ◽  
Locally Compact Group ◽  
Necessary And Sufficient Conditions ◽  
Locally Compact ◽  
Necessary And Sufficient

AbstractWe have recently shown that, for 2 < p < ∞, a locally compact group G is compact if and only if the convolution multiplication f * g exists for all f, g ∈ L p(G). Here, we study the existence of f * g for all f, g ∈ L p(G) in the case where 0 < p ≤ 2. Also, for 0 < p < ∞, we offer some necessary and sufficient conditions for L p(G) * L p(G) to be contained in certain function spaces on G.

scholarly journals A metrizable semitopological semilattice with non-closed partial order

2020 ◽  
Vol 8 (1) ◽  
pp. 67-75
Author(s):  
Taras Banakh ◽  
Serhii Bardyla ◽  
Alex Ravsky
Keyword(s):  
Partial Order ◽  
Dense Subset ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Countable Family ◽  
Hausdorff Topology ◽  
Necessary And Sufficient ◽  
Convergent Sequences

AbstractWe construct a metrizable semitopological semilattice X whose partial order P = {(x, y) ∈ X × X : xy = x} is a non-closed dense subset of X × X. As a by-product we find necessary and sufficient conditions for the existence of a (metrizable) Hausdorff topology on a set, act, semigroup or semilattice, having a prescribed countable family of convergent sequences.

scholarly journals Pseudo-contractibility Of Weighted Lp -Algebras

2013 ◽  
Vol 21 (3) ◽  
pp. 5-16
Author(s):  
Fatemeh Abtahi
Keyword(s):  
Weight Function ◽  
Compact Group ◽  
Sufficient Conditions ◽  
Locally Compact Group ◽  
Necessary And Sufficient Conditions ◽  
Locally Compact ◽  
Necessary And Sufficient ◽  
Group 1

Abstract Let G be a locally compact group, 1 < p < ∞ and let ω be a weight function on G. Recently, we introduced the Lebesgue weighted Lp-algebra L1pω(G). Here, we establish necessary and sufficient conditions for L1pω(G) to be φ-contractible, pseudo-contractible or contractible. Moreover we give some similar results about LP(G, ω).

scholarly journals Speedups of ergodic group extensions

2012 ◽  
Vol 33 (4) ◽  
pp. 969-982 ◽  
Author(s):  
ANDREY BABICHEV ◽  
ROBERT M. BURTON ◽  
ADAM FIELDSTEEL
Keyword(s):  
Sufficient Conditions ◽  
Countable Group ◽  
Necessary And Sufficient Conditions ◽  
Locally Compact ◽  
Group Extensions ◽  
Necessary And Sufficient

AbstractWe prove that for all ergodic extensions $S_{1}$ of a transformation by a locally compact second countable group $G$, and for all $G$-extensions $ S_{2} $ of an aperiodic transformation, there is a relative speedup of $ S_{1} $ that is relatively isomorphic to $S_{2}$. We apply this result to give necessary and sufficient conditions for two ergodic $n$-point or countable extensions to be related in this way.

scholarly journals Finiteness at infinity

1971 ◽  
Vol 17 (4) ◽  
pp. 299-304 ◽  
Author(s):  
P. A. Firby
Keyword(s):  
Topological Space ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Locally Compact ◽  
Necessary And Sufficient ◽  
Tychonoff Spaces

If X is a Tychonoff topological space, and if βX is the Stone-Cech compactification of X, then βX\X will denote the complement of X in βX. If A is a subset of X, then cl [A: X] will denote the closure of A in X, and int [A: X] will denote the interior of A in X. In Isbell ((3), p. 119) a property of βX\X is called a property which X has at infinity, and it is the aim of this paper to give necessary and sufficient conditions for X to be finite at infinity. Since βX is T1 we can say that if X is finite at infinity, then βX\X is closed in βX. So we lose nothing by restricting our attention to locally compact, Tychonoff spaces, and for the remainder of the paper X will denote such a space.

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