Posted on

Actions of Discrete Amenable Groups on von Neumann Algebras by Adrian Ocneanu

By Adrian Ocneanu

Show description

Read Online or Download Actions of Discrete Amenable Groups on von Neumann Algebras PDF

Similar linear books

Dynamical Entropy in Operator Algebras (Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge A Series of Modern Surveys in Mathematics)

The booklet addresses mathematicians and physicists, together with graduate scholars, who're attracted to quantum dynamical platforms and functions of operator algebras and ergodic thought. it's the basically monograph in this subject. even supposing the authors think a simple wisdom of operator algebras, they offer particular definitions of the notions and usually entire proofs of the consequences that are used.

Positive Operator Semigroups: From Finite to Infinite Dimensions

This publication supplies a steady yet up to date creation into the speculation of operator semigroups (or linear dynamical systems), which are used with nice luck to explain the dynamics of advanced phenomena bobbing up in lots of purposes. Positivity is a estate which obviously appears to be like in actual, chemical, organic or financial tactics.

Extra info for Actions of Discrete Amenable Groups on von Neumann Algebras

Sample text

Q , which invariant Let Trick. ,q I~ ~ 6 k=l generating be a separable all the projections by the automorphisms ~: e ÷ M W If C (9) and thus prove the 1 be unitaries and let does not with O {Ad U m l m E I N } C Aut M e. 5 to the projec- a family (n) . (n) < 1 e k ~g ~e k ) I~ n ' = {~gigEG} and in detail. let us choose (n) ek = le(k0) Step C is proved. small, to make y = 0 in this procedure N ' N M~ k such that k, thus e0 = fq+ I, can be taken arbitrarily Let us describe N'A M e . ,q, gE K (i + IKI)-I Ifkl~ Ifk+ll#~< ( i - ( i + Step D.

Connes. y E S' n M~ Te(la[ 2) in nontrivial B~(z) - z ~ 0. M, and But Bk(p) IBe(z) -zl 2 # 0. and q = k ~ zBk(P)" B(q) = q, there is qlB~(z) - zl 2 ~ 0 , Let x= (B~k(z); then plBe(x) - x I ~ 0. We n o w use the Slow R e i n d e x a t i o n N the s m a l l e s t contains x, W*-subalgebra and let and the c o u n t a b l e y e S' A Me, F Me S. a(y) We send = B~(Y) Te(la*1218w(y)-yl F r o m our choice that A Let of x ~ = {~,B w} 6 A u t ( M e ) , leaves be the sub W * - a l g e b r a subset ya = a y , of Trick.

F; In v i e w of (Ei, k) to The only p r o b l e m is the fact that we alter the old tower. If f was e - i n v a r i a n t then cutting with l-f w o u l d not affect a E. We approximate this by taking a tower indexed by a very large subset K' of G; such a tower has a very good global invariance, we regroup its p r o j e c t i o n s to get the tower For G=~, I = {i} and (fi,k) and s u b s e q u e n t l y indexed by K I .... ,KN- K l = {1,2 ..... p} c ~, a typical picture w o u l d be the following: X Z mp ......

Download PDF sample

Rated 4.90 of 5 – based on 19 votes