scholarly journals Prime Poisson suspensions

2014 ◽  
Vol 35 (7) ◽  
pp. 2216-2230 ◽  
Author(s):  
FRANÇOIS PARREAU ◽  
EMMANUEL ROY
Keyword(s):  
Compact Group ◽  
Fock Space ◽  
Space Structure ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Infinite Measure ◽  
Necessary And Sufficient ◽  
Group Rotations

We establish a necessary and sufficient condition for a Poisson suspension to be prime. The proof is based on the Fock space structure of the $L^{2}$-space of the Poisson suspension. We give examples of explicit infinite measure-preserving systems, in particular of non-singular compact group rotations that give rise to prime Poisson suspensions. We also compare some properties of so far known prime transformations with those of our examples, showing that these examples are new.

Strongly equivalent invariant measures

1980 ◽  
Vol 88 (1) ◽  
pp. 33-43 ◽  
Author(s):  
J. Rosenblatt
Keyword(s):  
Measure Space ◽  
Positive Measure ◽  
Invariant Measures ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Zero Measure ◽  
Infinite Measure ◽  
Two Measures ◽  
Necessary And Sufficient

AbstractTwo measures are strongly equivalent if they have the same sets of zero measure and the same sets of infinite measure. Given a group G of strongly non-singular measurable transformations of a non-atomic positive measure space (X, β, p), if G is amenable, then a necessary and sufficient condition for there to be a G-invariant positive measure on (X, β) which is strongly equivalent to p is that p(E) > 0 implies inf p(gE) > 0 and also p(E) < ∞ implies

scholarly journals A LIMIT THEOREM FOR OCCUPATION MEASURES OF LÉVY PROCESSES IN COMPACT GROUPS

2012 ◽  
Vol 13 (01) ◽  
pp. 1250008
Author(s):  
ARNO BERGER ◽  
STEVEN N. EVANS
Keyword(s):  
Limit Theorem ◽  
Dynamical Systems ◽  
Compact Group ◽  
Short Proof ◽  
Compact Groups ◽  
Sufficient Condition ◽  
Occupation Measure ◽  
Necessary And Sufficient Condition ◽  
Occupation Measures ◽  
Necessary And Sufficient

A short proof utilizing dynamical systems techniques is given of a necessary and sufficient condition for the normalized occupation measure of a Lévy process in a metrizable compact group to be asymptotically uniform with probability one.

Hecke **-algebras on locally compact hypergroups

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Seyyed Mohammad Tabatabaie ◽  
Bentolhoda Sadathoseyni
Keyword(s):  
Compact Group ◽  
Hecke Algebras ◽  
Locally Compact Group ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Locally Compact ◽  
Basic Properties ◽  
Necessary And Sufficient

AbstractIn this paper, for a discrete hypergroup K and its subhypergroup H, we initiate the related Hecke {*}-algebra which is an extension of the classical one, and study its basic properties. Especially, we give a necessary and sufficient condition (named (β)) for this algebra to be associative. Also, we show that this new structure is an associative {*}-algebra if and only if K is a locally compact group.

scholarly journals Some properties of distal actions on locally compact groups

2017 ◽  
Vol 39 (5) ◽  
pp. 1340-1360 ◽  
Author(s):  
C. R. E. RAJA ◽  
RIDDHI SHAH
Keyword(s):  
Compact Group ◽  
Locally Compact Group ◽  
Locally Compact Groups ◽  
Compact Groups ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Locally Compact ◽  
Necessary And Sufficient ◽  
Contraction Group

We consider the actions of (semi)groups on a locally compact group by automorphisms. We show the equivalence of distality and pointwise distality for the actions of a certain class of groups. We obtain a decomposition for contraction groups of an automorphism under certain conditions. We give a necessary and sufficient condition for distality of an automorphism in terms of its contraction group. We compare classes of (pointwise) distal groups and groups whose closed subgroups are unimodular. In particular, we study relations between distality, unimodularity and contraction subgroups.

scholarly journals Limits of Characters of Wreath Products 𝔖n(T) of a Compact Group T With the Symmetric Groups and Characters of 𝔖∞(T), I

2009 ◽  
Vol 193 ◽  
pp. 1-93
Author(s):  
Takeshi Hirai ◽  
Etsuko Hirai ◽  
Akihito Hora
Keyword(s):  
Compact Group ◽  
Symmetric Groups ◽  
Wreath Products ◽  
Continuous Limit ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Irreducible Characters ◽  
Induced Representations ◽  
Irreducible Components ◽  
Necessary And Sufficient

AbstractIn the first half of this paper, all the limits of irreducible characters of Gn = 𝔖n(T) as n → ∞ are calculated. The set of all continuous limit functions on G = 𝔖 ∞(T) is exactly equal to the set of all characters of G determined in [HH6]. We give a necessary and sufficient condition for a series of irreducible characters of Gn to have a continuous limit and also such a condition to have a discontinuous limit. In the second half, we study the limits of characters of certain induced representations of Gn which are usually reducible. The limits turn out to be characters of G, and we analyse which of irreducible components are responsible to these limits.

A Proposed Framework Emphasizing Auditor Reliability over Auditor Independence

2003 ◽  
Vol 17 (3) ◽  
pp. 257-266 ◽  
Author(s):  
Mark H. Taylor ◽  
F. Todd DeZoort ◽  
Edward Munn ◽  
Martha Wetterhall Thomas
Keyword(s):  
Public Interest ◽  
Auditor Independence ◽  
Public Confidence ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Accounting Profession ◽  
The Public ◽  
Necessary And Sufficient

This paper introduces an auditor reliability framework that repositions the role of auditor independence in the accounting profession. The framework is motivated in part by widespread confusion about independence and the auditing profession's continuing problems with managing independence and inspiring public confidence. We use philosophical, theoretical, and professional arguments to argue that the public interest will be best served by reprioritizing professional and ethical objectives to establish reliability in fact and appearance as the cornerstone of the profession, rather than relationship-based independence in fact and appearance. This revised framework requires three foundation elements to control subjectivity in auditors' judgments and decisions: independence, integrity, and expertise. Each element is a necessary but not sufficient condition for maximizing objectivity. Objectivity, in turn, is a necessary and sufficient condition for achieving and maintaining reliability in fact and appearance.

The Power of Public Positions

2018 ◽  
Author(s):  
Thomas Sinclair
Keyword(s):  
Detailed Analysis ◽  
Political Authority ◽  
The State ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
State Institutions ◽  
State Of Nature ◽  
Necessary And Sufficient

The Kantian account of political authority holds that the state is a necessary and sufficient condition of our freedom. We cannot be free outside the state, Kantians argue, because any attempt to have the “acquired rights” necessary for our freedom implicates us in objectionable relations of dependence on private judgment. Only in the state can this problem be overcome. But it is not clear how mere institutions could make the necessary difference, and contemporary Kantians have not offered compelling explanations. A detailed analysis is presented of the problems Kantians identify with the state of nature and the objections they face in claiming that the state overcomes them. A response is sketched on behalf of Kantians. The key idea is that under state institutions, a person can make claims of acquired right without presupposing that she is by nature exceptional in her capacity to bind others.

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