scholarly journals The maximal coarse Baum–Connes conjecture for spaces which admit a fibred coarse embedding into Hilbert space

2013 ◽  
Vol 249 ◽  
pp. 88-130 ◽  
Author(s):  
Xiaoman Chen ◽  
Qin Wang ◽  
Guoliang Yu
Keyword(s):  
Hilbert Space ◽  
Coarse Embedding

scholarly journals Straightening warped cones

2020 ◽  
pp. 1-25 ◽  
Author(s):  
Damian Sawicki ◽  
Jianchao Wu
Keyword(s):  
Hilbert Space ◽  
Banach Spaces ◽  
Free Action ◽  
Property A ◽  
Coarse Embedding

We provide the converses to two results of Roe [Warped cones and property A, Geom. Topol. 9 (2005) 163–178, https://doi.org/10.2140/9t.2005.9.163 ]: first, the warped cone associated to a free action of an a-T-menable group admits a fibered coarse embedding into a Hilbert space, and second, a free action yielding a warped cone with property A must be amenable. We construct examples showing that in both cases the freeness assumption is necessary. The first equivalence is obtained also for other classes of Banach spaces, in particular for [Formula: see text]-spaces.

scholarly journals Admitting a Coarse Embedding is Not Preserved Under Group Extensions

2018 ◽  
Vol 2019 (20) ◽  
pp. 6480-6498 ◽  
Author(s):  
Goulnara Arzhantseva ◽  
Romain Tessera
Keyword(s):  
Hilbert Space ◽  
Finitely Generated ◽  
Group Extensions ◽  
Finitely Generated Group ◽  
Finitely Generated Groups ◽  
Coarse Embedding ◽  
Monster Group

AbstractWe construct a finitely generated group which is an extension of two finitely generated groups coarsely embeddable into Hilbert space but which itself does not coarsely embed into Hilbert space. Our construction also provides a new infinite monster group: the first example of a finitely generated group that does not coarsely embed into Hilbert space and yet does not contain a weakly embedded expander.

Hilbert Space

1993 ◽  
Author(s):  
J. R. Retherford
Keyword(s):  
Hilbert Space

On Definition of Expansion Probabilistic Hilbert Space

2018 ◽  
Vol 14 (3) ◽  
pp. 59-73
Author(s):  
Ahmed Hasan Hamed ◽  
Keyword(s):  
Hilbert Space ◽  
Definition Of
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