scholarly journals Weak⁎ fixed point property and asymptotic centre for the Fourier–Stieltjes algebra of a locally compact group

2013 ◽  
Vol 264 (1) ◽  
pp. 288-302 ◽  
Author(s):  
Gero Fendler ◽  
Anthony To-Ming Lau ◽  
Michael Leinert
Keyword(s):  
Fixed Point ◽  
Compact Group ◽  
Locally Compact Group ◽  
Fixed Point Property ◽  
Point Property ◽  
Locally Compact

scholarly journals Rigidity theory for C∗-dynamical systems and the “Pedersen Rigidity Problem”, II

2019 ◽  
Vol 30 (08) ◽  
pp. 1950038
Author(s):  
S. Kaliszewski ◽  
Tron Omland ◽  
John Quigg
Keyword(s):  
Fixed Point ◽  
Dynamical Systems ◽  
Compact Group ◽  
Related Problem ◽  
Locally Compact Group ◽  
Crossed Products ◽  
Locally Compact ◽  
Fixed Point Algebra ◽  
Multiplier Algebras

This is a follow-up to a paper with the same title and by the same authors. In that paper, all groups were assumed to be abelian, and we are now aiming to generalize the results to nonabelian groups. The motivating point is Pedersen’s theorem, which does hold for an arbitrary locally compact group [Formula: see text], saying that two actions [Formula: see text] and [Formula: see text] of [Formula: see text] are outer conjugate if and only if the dual coactions [Formula: see text] and [Formula: see text] of [Formula: see text] are conjugate via an isomorphism that maps the image of [Formula: see text] onto the image of [Formula: see text] (inside the multiplier algebras of the respective crossed products). We do not know of any examples of a pair of non-outer-conjugate actions such that their dual coactions are conjugate, and our interest is therefore exploring the necessity of latter condition involving the images; and we have decided to use the term “Pedersen rigid” for cases where this condition is indeed redundant. There is also a related problem, concerning the possibility of a so-called equivariant coaction having a unique generalized fixed-point algebra, that we call “fixed-point rigidity”. In particular, if the dual coaction of an action is fixed-point rigid, then the action itself is Pedersen rigid, and no example of non-fixed-point-rigid coaction is known.

scholarly journals Amenable locally compact semigroups and a fixed point property

2018 ◽  
Vol 19 (1) ◽  
pp. 3-12
Author(s):  
Fatemeh Akhtari ◽  
◽  
Rasoul Nasr-Isfahani ◽  
Keyword(s):  
Fixed Point ◽  
Fixed Point Property ◽  
Point Property ◽  
Locally Compact ◽  
Compact Semigroups ◽  
Locally Compact Semigroups

scholarly journals Fixed point characterization of left amenable Lau algebras

2004 ◽  
Vol 2004 (62) ◽  
pp. 3333-3338 ◽  
Author(s):  
R. Nasr-Isfahani
Keyword(s):  
Fixed Point ◽  
Banach Algebras ◽  
Locally Compact Group ◽  
Compact Groups ◽  
Fourier Algebra ◽  
Measure Algebra ◽  
Point Property ◽  
Locally Compact ◽  
Wide Range

The present paper deals with the concept of left amenability for a wide range of Banach algebras known as Lau algebras. It gives a fixed point property characterizing left amenable Lau algebras𝒜in terms of left Banach𝒜-modules. It also offers an application of this result to some Lau algebras related to a locally compact groupG, such as the Eymard-Fourier algebraA(G), the Fourier-Stieltjes algebraB(G), the group algebraL1(G), and the measure algebraM(G). In particular, it presents some equivalent statements which characterize amenability of locally compact groups.

scholarly journals Interpolation in wavelet spaces and the HRT-conjecture

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Eirik Berge
Keyword(s):  
Compact Group ◽  
Wavelet Transforms ◽  
Reproducing Kernel ◽  
Reproducing Kernel Hilbert Space ◽  
Space Structure ◽  
Locally Compact Group ◽  
Locally Compact ◽  
Positive Type ◽  
Time Frequency ◽  
Hrt Conjecture

AbstractWe investigate the wavelet spaces $$\mathcal {W}_{g}(\mathcal {H}_{\pi })\subset L^{2}(G)$$ W g ( H π ) ⊂ L 2 ( G ) arising from square integrable representations $$\pi :G \rightarrow \mathcal {U}(\mathcal {H}_{\pi })$$ π : G → U ( H π ) of a locally compact group G. We show that the wavelet spaces are rigid in the sense that non-trivial intersection between them imposes strong restrictions. Moreover, we use this to derive consequences for wavelet transforms related to convexity and functions of positive type. Motivated by the reproducing kernel Hilbert space structure of wavelet spaces we examine an interpolation problem. In the setting of time–frequency analysis, this problem turns out to be equivalent to the HRT-conjecture. Finally, we consider the problem of whether all the wavelet spaces $$\mathcal {W}_{g}(\mathcal {H}_{\pi })$$ W g ( H π ) of a locally compact group G collectively exhaust the ambient space $$L^{2}(G)$$ L 2 ( G ) . We show that the answer is affirmative for compact groups, while negative for the reduced Heisenberg group.

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