Non-unitarizable uniformly bounded group representations

1996 ◽  
pp. 30-52
Author(s):  
Gilles Pisier
Keyword(s):  
Group Representations ◽  
Bounded Group ◽  
Uniformly Bounded

scholarly journals AN ALGEBRA WHOSE SUBALGEBRAS ARE CHARACTERIZED BY DENSITY

2015 ◽  
Vol 80 (3) ◽  
pp. 1066-1074 ◽  
Author(s):  
ALESSANDRO VIGNATI
Keyword(s):  
Operator Algebra ◽  
Group Representation ◽  
Bounded Group ◽  
Image Position ◽  
Uniformly Bounded

AbstractWe refine a construction of Choi, Farah, and Ozawa to build a nonseparable amenable operator algebra ${\rm {\cal A}}$ ⊆ ℓ∞ (M2) whose nonseparable subalgebras, including ${\rm {\cal A}}$, are not isomorphic to a C*-algebra. This is done using a Luzin gap and a uniformly bounded group representation.Next, we study additional properties of ${\rm {\cal A}}$ and of its separable subalgebras, related to the Kadison Kastler metric.

scholarly journals Joseph Fourier 250thBirthday: Modern Fourier Analysis and Fourier Heat Equation in Information Sciences for the XXIst Century

Entropy ◽  
2019 ◽  
Vol 21 (3) ◽  
pp. 250
Author(s):  
Frédéric Barbaresco ◽  
Jean-Pierre Gazeau
Keyword(s):  
Fourier Analysis ◽  
Heat Equation ◽  
Harmonic Analysis ◽  
Lie Groups ◽  
Coherent States ◽  
Geometric Theory ◽  
Plancherel Formula ◽  
Group Representations ◽  
Modern Development ◽  
Xxist Century

For the 250th birthday of Joseph Fourier, born in 1768 at Auxerre in France, this MDPI special issue will explore modern topics related to Fourier analysis and Fourier Heat Equation. Fourier analysis, named after Joseph Fourier, addresses classically commutative harmonic analysis. The modern development of Fourier analysis during XXth century has explored the generalization of Fourier and Fourier-Plancherel formula for non-commutative harmonic analysis, applied to locally compact non-Abelian groups. In parallel, the theory of coherent states and wavelets has been generalized over Lie groups (by associating coherent states to group representations that are square integrable over a homogeneous space). The name of Joseph Fourier is also inseparable from the study of mathematics of heat. Modern research on Heat equation explores geometric extension of classical diffusion equation on Riemannian, sub-Riemannian manifolds, and Lie groups. The heat equation for a general volume form that not necessarily coincides with the Riemannian one is useful in sub-Riemannian geometry, where a canonical volume only exists in certain cases. A new geometric theory of heat is emerging by applying geometric mechanics tools extended for statistical mechanics, for example, the Lie groups thermodynamics.

scholarly journals Crystallography: Symmetry groups and group representations

2012 ◽  
Vol 22 ◽  
pp. 00006
Author(s):  
B. Grenier ◽  
R. Ballou
Keyword(s):  
Symmetry Groups ◽  
Group Representations

scholarly journals Probing charge pumping and relaxation of the chiral anomaly in a Dirac semimetal

2021 ◽  
Vol 7 (16) ◽  
pp. eabg0914
Author(s):  
Bing Cheng ◽  
Timo Schumann ◽  
Susanne Stemmer ◽  
N. P. Armitage
Keyword(s):  
Terahertz Spectroscopy ◽  
Point Group ◽  
Spectral Weight ◽  
Chiral Anomaly ◽  
Group Representations ◽  
Field Independence ◽  
Transport Channel ◽  
Scattering Rate ◽  
Chiral Magnetic Effect ◽  
A Charge

The linear band crossings of 3D Dirac and Weyl semimetals are characterized by a charge chirality, the parallel or antiparallel locking of electron spin to its momentum. These materials are believed to exhibit an E · B chiral magnetic effect that is associated with the near conservation of chiral charge. Here, we use magneto-terahertz spectroscopy to study epitaxial Cd3As2 films and extract their conductivities σ(ω) as a function of E · B. As field is applied, we observe a markedly sharp Drude response that rises out of the broader background. Its appearance is a definitive signature of a new transport channel and consistent with the chiral response, with its spectral weight a measure of the net chiral charge and width a measure of the scattering rate between chiral species. The field independence of the chiral relaxation establishes that it is set by the approximate conservation of the isospin that labels the crystalline point-group representations.

scholarly journals Some Conditions under Which Sequences of Functions are Uniformly Bounded

1968 ◽  
Vol 33 ◽  
pp. 75-83
Author(s):  
D.C. Rung
Keyword(s):  
Complex Analysis ◽  
Normal Family ◽  
Normal Families ◽  
Usual Pattern ◽  
Uniformly Bounded

After one introduces the theory of normal families in a course in complex analysis, the usual pattern is to give an example of a non-normal family. One of the simplest, of course, is the sequence fn(z) = nz, n = 1,2, ···. The very devastating effect of multiplying by zero insures the required abnormality!

Group representations which vanish at infinity

1980 ◽  
Vol 251 (2) ◽  
pp. 185-190 ◽  
Author(s):  
Keith F. Taylor
Keyword(s):  
Group Representations
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