A characterization of locally compact amenable groups by means of tensor products

1989 ◽  
Vol 52 (5) ◽  
pp. 424-427 ◽  
Author(s):  
Mohammed E. B. Bekka
Keyword(s):  
Tensor Products ◽  
Locally Compact ◽  
Amenable Groups

A characterization of locally compact inner amenable groups

2008 ◽  
Vol 28 (3) ◽  
pp. 588-594 ◽  
Author(s):  
Ali Ghaffari
Keyword(s):  
Locally Compact ◽  
Amenable Groups

Scaling sets and generalized scaling sets on Cantor dyadic group

2020 ◽  
Vol 18 (04) ◽  
pp. 2050019
Author(s):  
Prasadini Mahapatra ◽  
Divya Singh
Keyword(s):  
Abelian Groups ◽  
Real Case ◽  
Locally Compact ◽  
Wavelet Sets ◽  
Locally Compact Abelian Groups ◽  
Dyadic Group ◽  
Compact Abelian Groups ◽  
Cantor Dyadic Group

Scaling and generalized scaling sets determine wavelet sets and hence wavelets. In real case, wavelet sets were proved to be an important tool for the construction of MRA as well as non-MRA wavelets. However, any result related to scaling/generalized scaling sets is not available in case of locally compact abelian groups. This paper gives a characterization of scaling sets and its generalized version along with relevant examples in dual Cantor dyadic group [Formula: see text]. These results can further be generalized to arbitrary locally compact abelian groups.

scholarly journals Criteria of closedness of nilradicals in zero dimensional locally compact rings

2021 ◽  
Vol 38 (1) ◽  
pp. 223-230
Author(s):  
MIHAIL URSUL ◽  
◽  
JOHN LANTA ◽  
Keyword(s):  
Locally Compact ◽  
Locally Finite ◽  
Totally Disconnected

We study in this paper conditions under which nilradicals of totally disconnected locally compact rings are closed. In the paper is given a characterization of locally finite compact rings via identities.

scholarly journals Continuity of Convolution of Test Functions on Lie Groups

2014 ◽  
Vol 66 (1) ◽  
pp. 102-140
Author(s):  
Lidia Birth ◽  
Helge Glöckner
Keyword(s):  
Continuous Functions ◽  
Locally Convex Space ◽  
Locally Compact Group ◽  
Locally Convex Spaces ◽  
Test Functions ◽  
Bilinear Map ◽  
Locally Compact ◽  
Compactly Supported ◽  
Locally Convex

AbstractFor a Lie group G, we show that the map taking a pair of test functions to their convolution, is continuous if and only if G is σ-compact. More generally, consider with t ≤ r + s, locally convex spaces E1, E2 and a continuous bilinear map b : E1 × E2 → F to a complete locally convex space F. Let be the associated convolution map. The main result is a characterization of those (G; r; s; t; b) for which β is continuous. Convolution of compactly supported continuous functions on a locally compact group is also discussed as well as convolution of compactly supported L1-functions and convolution of compactly supported Radon measures.

scholarly journals A Note on Amenability of Locally Compact Quantum Groups

2014 ◽  
Vol 57 (2) ◽  
pp. 424-430 ◽  
Author(s):  
Piotr M. Sołtan ◽  
Ami Viselter
Keyword(s):  
Quantum Groups ◽  
Short Note ◽  
Locally Compact Groups ◽  
Compact Groups ◽  
Locally Compact ◽  
Locally Compact Quantum Groups ◽  
Compact Quantum Groups

AbstractIn this short note we introduce a notion called quantum injectivity of locally compact quantum groups, and prove that it is equivalent to amenability of the dual. In particular, this provides a new characterization of amenability of locally compact groups.

Pego everywhere

2016 ◽  
Vol 15 (04) ◽  
pp. 1650074 ◽  
Author(s):  
Przemysław Górka ◽  
Tomasz Kostrzewa
Keyword(s):  
Fourier Transform ◽  
Abelian Groups ◽  
General Version ◽  
Pontryagin Duality ◽  
Locally Compact ◽  
Locally Compact Abelian Groups ◽  
Compact Abelian Groups ◽  
The Fourier Transform ◽  
Compact Subsets

In this note we show the general version of Pego’s theorem on locally compact abelian groups. The proof relies on the Pontryagin duality as well as on the Arzela–Ascoli theorem. As a byproduct, we get the characterization of relatively compact subsets of [Formula: see text] in terms of the Fourier transform.

scholarly journals DOUBLE CROSSED PRODUCTS OF LOCALLY COMPACT QUANTUM GROUPS

2005 ◽  
Vol 4 (1) ◽  
pp. 135-173 ◽  
Author(s):  
Saad Baaj ◽  
Stefaan Vaes
Keyword(s):  
Quantum Group ◽  
Quantum Groups ◽  
Matched Pair ◽  
Crossed Products ◽  
Locally Compact ◽  
Locally Compact Quantum Groups ◽  
Algebraic Properties ◽  
Locally Compact Quantum Group ◽  
Compact Quantum Groups

For a matched pair of locally compact quantum groups, we construct the double crossed product as a locally compact quantum group. This construction generalizes Drinfeld’s quantum double construction. We study the modular theory and the $\mathrm{C}^*$-algebraic properties of these double crossed products, as well as several links between double crossed products and bicrossed products. In an appendix, we study the Radon–Nikodym derivative of a weight under a quantum group action (following Yamanouchi) and obtain, as a corollary, a new characterization of closed quantum subgroups. AMS 2000 Mathematics subject classification: Primary 46L89. Secondary 46L65

Følner Nets for Semidirect Products of Amenable Groups

2008 ◽  
Vol 51 (1) ◽  
pp. 60-66 ◽  
Author(s):  
David Janzen
Keyword(s):  
Strong Form ◽  
Locally Compact ◽  
Amenable Groups ◽  
Semidirect Products ◽  
Euclidean Motion ◽  
Motion Groups

AbstractFor unimodular semidirect products of locally compact amenable groups N and H, we show that one can always construct a Følner net of the form (Aα × Bβ) for G, where (Aα) is a strong form of Følner net for N and (Bβ) is any Følner net for H. Applications to the Heisenberg and Euclidean motion groups are provided.

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