scholarly journals A compactification of an orbit space

Filomat ◽  
2018 ◽  
Vol 32 (10) ◽  
pp. 3429-3434
Author(s):  
Dünya Karapınar
Keyword(s):  
Invariant Subspace ◽  
Discrete Group ◽  
Orbit Space ◽  
Maximal Ideals ◽  
Function Ring

Let X be a Tychonoff G-space, G be a finite discrete group and A be a dense and invariant subspace of X. In this paper, by means of Gelfand?s method, we construct a compactification of the orbit space A/G. As an application, we show that the set of maximal ideals of even function ring with Stone topology is a compactification of non-negative rationals.

scholarly journals On the Projective Cover of an orbit space

1989 ◽  
Vol 46 (2) ◽  
pp. 308-312 ◽  
Author(s):  
K. K. Azad ◽  
Gunjan Agrawal
Keyword(s):  
Projective Space ◽  
Discrete Group ◽  
Orbit Space ◽  
Projective Cover

AbstractIn this paper, we obtain the projective cover of the orbit space X/G in terms of the orbit space of the projective space of X, when X is a Tychonoff G-space and G is a finite discrete group. An example shows that finiteness of G is needed.

scholarly journals On the Stone-Čeck compactification of an orbit space

1987 ◽  
Vol 36 (3) ◽  
pp. 435-439 ◽  
Author(s):  
Kavita Srivastava
Keyword(s):  
Discrete Group ◽  
Orbit Space ◽  
Tychonoff Space ◽  
The Given

By extending the given action of a discrete group G on a Tychonoff space X to βX, it is proved that the Stone-Čech compactification of the orbit space of X is the orbit space of the Stone-Čech compactification βX of X, when G is finite. The notion of G-retractive spaces is introduced and it is proved that the orbit space of a G-retractive space with G finite, is G-retractive.

scholarly journals On maximal ideals in certain reduced twisted C*-crossed products

2015 ◽  
Vol 158 (3) ◽  
pp. 399-417 ◽  
Author(s):  
ERIK BÉDOS ◽  
ROBERTO CONTI
Keyword(s):  
Discrete Group ◽  
Crossed Product ◽  
Crossed Products ◽  
Bijective Correspondence ◽  
C Algebra ◽  
Maximal Ideals ◽  
Maximal Invariant

AbstractWe consider a twisted action of a discrete groupGon a unital C*-algebraAand give conditions ensuring that there is a bijective correspondence between the maximal invariant ideals ofAand the maximal ideals in the associated reduced C*-crossed product.

scholarly journals Topological Boundaries of Unitary Representations

2020 ◽  
Author(s):  
Alex Bearden ◽  
Mehrdad Kalantar
Keyword(s):  
Invariant Subspace ◽  
Unitary Representation ◽  
Discrete Group ◽  
Regular Representation ◽  
Unitary Representations ◽  
Algebra Structure

Abstract We introduce and study a generalization of the notion of the Furstenberg boundary of a discrete group $\Gamma $ to the setting of a general unitary representation $\pi : \Gamma \to B(\mathcal H_\pi )$. This space, which we call the “Furstenberg–Hamana boundary” (or "FH-boundary") of the pair $(\Gamma , \pi )$, is a $\Gamma $-invariant subspace of $B(\mathcal H_\pi )$ that carries a canonical $C^{\ast }$-algebra structure. In many natural cases, including when $\pi $ is a quasi-regular representation, the Furstenberg–Hamana boundary of $\pi $ is commutative but can be noncommutative in general. We study various properties of this boundary and discuss possible applications, for example in uniqueness of certain types of traces.

The range of block Hankel operators

Filomat ◽  
2018 ◽  
Vol 32 (9) ◽  
pp. 3237-3243
Author(s):  
In Hwang ◽  
In Kim ◽  
Sumin Kim
Keyword(s):  
Hardy Space ◽  
Invariant Subspace ◽  
Hankel Operators ◽  
Coprime Factorization ◽  
Backward Shift ◽  
Vector Valued

In this note we give a connection between the closure of the range of block Hankel operators acting on the vector-valued Hardy space H2Cn and the left coprime factorization of its symbol. Given a subset F ? H2Cn, we also consider the smallest invariant subspace S*F of the backward shift S* that contains F.

scholarly journals Local Anesthetic Delivered with a Dual Action Ring and Injection Applicator Reduces the Acute Pain Response of Lambs during Tail Docking

Animals ◽  
2021 ◽  
Vol 11 (8) ◽  
pp. 2242
Author(s):  
Alison Small ◽  
Danila Marini ◽  
Ian Colditz
Keyword(s):  
Acute Pain ◽  
Local Anesthetic ◽  
Dual Function ◽  
Treatment Groups ◽  
Ewe Lambs ◽  
Tail Docking ◽  
Function Ring ◽  
Dual Action ◽  
Abnormal Behaviors ◽  
Control Sham

Docking the tail of lambs is a standard husbandry procedure and is achieved through several techniques including clamps, hot or cold knives and latex rings, the last of which is the most popular. All tail docking methods cause acute pain which can be reduced by application of local anesthetic, however precise anatomical injection for optimal efficacy requires considerable skill. This pen trial evaluated the ability of local anesthetic (LA) delivered with a dual function ring applicator/injector to alleviate acute tail docking pain. Thirty ewe lambs were assigned to one of three treatment groups (n = 10 per group): ring plus local anesthetic (Ring LA), ring only (Ring) and sham handled control (Sham). Lambs were videoed and their behavior categorized every five minutes for the first hour and every 10 min for the subsequent two hours after treatment. There was a significant effect (p < 0.001) of treatment on total active pain related behaviors in the first hour, with Ring lambs showing higher counts compared to Ring LA or Sham. Ring lambs also displayed a significantly higher count of combined abnormal postures (p < 0.001) than Ring LA or Sham lambs. Delivery of 1.5 mL of 2% lignocaine via the dual action device abolished abnormal behaviors and signs of pain in Ring LA lambs. However, lambs in the Ring LA group spent less time attempting to suckle compared to Ring and Sham lambs, suggesting that some residual discomfort remained.

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