1550075568-C-Algebras_and_Finite-Dimensional_Approximations__Brown_

F. Bimodules over von Neumann Algebras 485 Proof. (1) =?- (2): By condition (1), there exist a finite 'subset ~ C M and E > 0 ...

486 F. Bimodules over van Neumann Algebras may assume that uo = f o = f. Then, for every unitary element w E B, we have L llEA(v ...

F. Bimodules over von Neumann Algebras 487 Wn E En such that llEAn (xjwnxi) 112 :S n-^1 for every i, j :S n. Let B1 = ClN and su ...

488 F. Bimodules over von Neumann Algebras Since Bis maximal abelian, we have Ji := vv* E B. Let N = B(f Bf)' neM e. Since Ae C ...

F. Bimodules over von Neumann Algebras 489 j,k,k' for every x EB (and, in particular, uu* = L,k,k' Wk,k'eowk,k' = 1). D Lemma F. ...

490 F. Bimodules over von Neumann Algebras Exercises Exercise F.l. Let 1i be an M-N-bimodule and e E 1i be a unit vector such th ...

F. Bimodules over von Neumann Algebras 491 References. The study of bimodules was emphasized by A. Connes [44] and developed by ...

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Bibliography C.A. Akemann, J. Anderson and G.K. Pedersen, Excising states of C* -algebras, Canad. J. Math. 38 (1986), 1239-1260 ...

494 Bibliography G.C. Bell, Property A for groups acting on metric spaces, Topology Appl. 130 (2003), 239-251. B. Blackadar, No ...

Bibliography 495 M.D. Choi and E.G. Effros, The completely positive lifting problem for C*-algebras, Ann. of Math. 104 (1976), ...

496 Bibliography E.G. Effros and E.C. Lance, Tensor products of operator algebras, Adv. Math. 25 (1977), no. 1, 1-34. E.G. Effr ...

Bibliography 497 P. de la Harpe, A.G. Robertson and A. Valette, On the spectrum of the sum of generators for a finitely generat ...

498 Bibliography E. Kirchberg and N.C. Phillips, Embedding of exact C' -algebras in the Cuntz algebra 02 , J. Reine Angew. Math ...

Bibliography 499 A. Olshanskii, SQ-universality of hyperbolic groups, Sb. Math. 186 (1995), 1199 - N. Ozawa, Amenable actions ...

500 Bibliography G. Pisier, Introduction to operator space theory, London Mathematical Society Lec- ture Note Series, 294. Camb ...

Bibliography 501 A.M. Sinclair and R.R. Smith, The Haagerup invariant for tensor products of oper- ator spaces. Math. Proc. Cam ...

502 Bibliography S. Wassermann, A separable quasidiagonal C* -algebra with a nonquasidiagonal quo- tient by the compact operato ...

Notation Index A (unitization of a C-algebra), 28 A, B, C and D (C-algebras), 2 A® B (minimal tensor product), 73 A ®max B (maxi ...

504 SA (suspension over a C*-algebra A), 251 s.f (s.f(t) = f(s-^1 t)), 42 T(H) (Toeplitz-Pimsner algebra), 142 Tr (nonnormalized ...