# A groupoid approach to C* - algebras - download pdf or read online By Jean Renault

ISBN-10: 3540099778

ISBN-13: 9783540099772

Read or Download A groupoid approach to C* - algebras PDF

Similar abstract books

Algebraic Groups and Class Fields - download pdf or read online

Precis of the most effects. - Algebraic Curves. - Maps From a Curve to a Commutative staff. - Singular Algebraic Curves. - Generalized Jacobians. - category box idea. - workforce Extension and Cohomology. - Bibliography. - Supplementary Bibliography. - Index.

Lattice Theory: Special Topics and Applications: Volume 2 - download pdf or read online

George Grätzer's Lattice thought: origin is his 3rd e-book on lattice conception (General Lattice conception, 1978, moment version, 1998). In 2009, Grätzer thought of updating the second one variation to mirror a few interesting and deep advancements. He quickly discovered that to put the basis, to survey the modern box, to pose examine difficulties, will require a couple of quantity and a couple of individual.

Ergodic Theory: Independence and Dichotomies by David Kerr, Hanfeng Li PDF

This e-book presents an advent to the ergodic conception and topological dynamics of activities of countable teams. it's equipped round the subject matter of probabilistic and combinatorial independence, and highlights the complementary roles of the asymptotic and the perturbative in its entire remedy of the middle strategies of susceptible blending, compactness, entropy, and amenability.

Additional resources for A groupoid approach to C* - algebras

Sample text

Let G be a t o p o l o g i c a l groupoid with open range map, A a t o p o l o - g i c a l group and c ~ ZI(G,A). Then (i) R (c) is a closed subgroup of A, T(c) is a subgroup of A, and R (c) and T(c) are orthogonal to each o t h e r . (ii) (iii) R (c) and T(c) depend o n l y on the class o f c. R (e) = {e} and T(e) = A, where e denotes the i d e n t i t y element of A as well as the constant cocycle e(x) = e. Proof : (i) Let us f i r s t show t h a t R(c) R (c) c R(c). Suppose a c R ( c ) and b e R (c).

The T-set of c is T(c) = {x E A : xoC E BI(G,~)}. The f o l l o w i n g p r o p o s i t i o n gives some basic p r o p e r t i e s of the q u a n t i t i e s R (c) and T(c) ; in p a r t i c u l a r , they depend o n l y on the cohomology class o f c. The aim o f t h i s section is to show t h e i r usefulness, j u s t i f y i n g t h e i r i n t r o d u c t i o n . Further references to the asymptotic range and the T-set o f a cocycle can be found in  in the context of ergodic theory. 5. Proposition : introof tensor products of f a c t o r s o f type I.

One of the main j u s t i f i c a t i o n s f o r i t s i n t r o d u c t i o n , besides the need to deal with projective representations, is given in Section 4, where the C * - a l g e b r a of an r - d i s c r e t e p r i n c i p a l groupoid is characterized, under s u i t a b l e conditions, by the existence of a p a r t i c u l a r l y nice kind of maximal abelian subalgebra. One of these conditions is amenability, which is defined in Section 3. 48 An essential tool in the study of the C * - a l g e b r a of a groupoid is the correspondence, very f a m i l i a r in the case of a group, between the u n i t a r y representations of the groupoid and the non-degenerate representations of the C * - a l g e b r a .

Download PDF sample

### A groupoid approach to C* - algebras by Jean Renault

by William
4.2

Rated 4.61 of 5 – based on 17 votes