1550075568-C-Algebras_and_Finite-Dimensional_Approximations__Brown_

13.4. Nonsemisplit extensions 385 Exercise 13.3.7. Use the previous result and Exercise 6.2.4 to show that the QWEP conjecture i ...

386 13. WEP and LLP Lemma 13.4.3. For every x E J, a E F and f E Co(O, 1], we have (1) limn-+oo llPn(f)xll = 0, (2) PnU)a - fa E ...

13.4. Nonsemisplit extensions 387 CJ into E9~=l Mn(<C), and the c.c.p. map W 0 idn induces an isometric *-homomorphism 7r: Pr ...

388 13. WEP and LLP tensor product): 0 ~ JK ®max F ~ B ®max F ~ CA ®max F -----?>- 0 l l l 0 __ _,,_ lK ® F -----,,.. B ® F _ ...

13.5. Norms on Jlll(.e^2 ) 8 llll(.e^2 ) 389 for ( E JC. Under this identification, x ® fj E llll(H ®JC) acts on S2(JC, 1-i) as ...

390 13. WEP and LLP generated by two elements and ISi can be 3.) Since EBm#n 7rm @1rn does not have a nonzero invariant vector, ...

13.6. References 391 It follows that C* ( {Vi : i = 1, ... , k}) c M / K cannot have an amenable tracial state (since, by Theore ...

...

Weakly Exact van Neumann Algebras Chapter 14 As noted earlier, if one defines exact van Neumann algebras as those which have a w ...

394 14. Weakly Exact von Neumann Algebras with M@ J C ker7r, the induced representation ii': M 0 (B / J) ----+ llll(H) is min-co ...

14.1. Defi.nition and examples 395 converges to if in the point-ultraweak topology. This implies the continuity of if. D Corolla ...

396 14. Weakly Exact von Neumann Algebras Remark 14.JL.7. Since there exists a discrete group which is not exact [71] (see also ...

14.2. Characterization of weak exactness 397 Proof. Let M be a von Neumann algebra with the W*OAP and let l.fJi be a net of fini ...

398 14. Weakly Exact von Neumann Algebras By assumption, 7r extends to a bi-normal *-homomorphism fr on M ® B**. Since M ®Jc ker ...

14.2. Characterization of weak exactness 399 Corollary 14.2.2. Let M be a weakly exact von Neumann algebra and X be an operator ...

400 14. Weakly Exact van Neumann Algebras (2) for any finite-dimensional operator system E in M, there exist se- quences of u.c. ...

14.2. Characterization of weak exactness 401 (3) =?-(1): The proof is virtually identical to that of Theorem 14.1.2. (2) =?-(3): ...

402 14. Weakly Exact von Neumann Algebras 1 1 1 :::; l~li;r1(2n + 2n-l + ... + 2m)[[a[[ =0, where the limits are taken along app ...

14.3. References 403 is a normal u.c.p. map such that (7/J o c,D)IMi®Mz = idMi®Mz· Hence the restriction <p of cp to M1 ®M2 C ...

...