Xiaoman Chen

Uniform embeddability and exactness of free products

Let A and B be countable discrete groups and let Γ=A∗B be their free product. We show that if both A and B are uniformly embeddable in a Hilbert space then so is Γ. We give two different proofs: the first directly constructs a uniform embedding of Γ from uniform embeddings of A and B; the second works without change to show that if both A and B are exact then so is Γ.

Spectral invariant subalgebras of reduced crossed product C∗-algebras ☆

AbstractLetG beadiscretegroupwithaproperlengthfunctionl: Inthispaper,weprovethattheSchwartz space S l2 ðG;AÞ is a spectral invariant dense subalgebra of the reduced crossedproduct C nr ðG;AÞ for all commutative C n -algebra A with a G-action if and only if G haspolynomialgrowthwithrespecttol:r 2002ElsevierScience(USA).Allrightsreserved. Keywords: ReducedcrossedproductC n -algebras;Spectralinvariantsubalgebras;Property(MRD) 0. IntroductionLetG beadiscretegroupwithalengthfunctionl: In[9],Jolissaintprovedthatthe Schwartzspace S l2 ðGÞ is a spectralinvariant dense subalgebra of the reducedgroupC n -algebraC n r ðGÞ ifG haspolynomialgrowthorG isthefundamentalgroupofanegativelycurvedcompactmanifold.In[4],delaHarpegeneralizedJolissaint’stheorem to all hyperbolic groups. Jolissaint and de la Harpe’s result plays animportantroleintheworkofConnes–MoscoviciontheNovikovconjecture[2]andtheworkofLafforgueontheBaum-Connesconjecture[10].Inthispaper,wegiveanecessaryandsufficientconditionfortheSchwartzspaceS

Rank Distributions on Coarse Spaces and Ideal Structure of Roe Algebras

The notions of controlled truncations for operators in the Roe algebras

Ideal structure of uniform Roe algebras of coarse spaces

C^*(X)

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

of a coarse space

Metric sparsification and operator norm localization

(X, \cal{E})

Ghost ideals in uniform Roe algebras of coarse spaces

with uniformly locally finite coarse structure, and rank distributions on

Characterization of the Haagerup property by fibred coarse embedding into Hilbert space

(X, \cal{E})

On finite decomposition complexity of Thompson group

are introduced. It is shown that the controlled propagation operators in an ideal

The coarse Novikov conjecture and Banach spaces with Property (H)

I