1550075568-C-Algebras_and_Finite-Dimensional_Approximations__Brown_

16.3. Resolution of Herrera's problem 425 Pn was finite-rank, we have Q(P,;{:1-i) = Q(7-i) (canonically) and the proof is comple ...

426 16. Herrera's Approximation Problem Proof. By Exercise 2.3.10 we may assume that T E Band(H). However, every banded operator ...

16.4. Counterexamples 427 After making this reduction, we consider the operator T E Mn(A) de- fined as follows: 0 bi 0 0 0 (^0 0 ...

428 16. Herrera's Approximation Problem there. For example, multiplying by T gives a nondiagonal matrix unit and similar fiddlin ...

16.5. References 429 The remainder of the proof is virtually identical to the proof of Proposi- tion 3.7.11. Indeed, if A is exa ...

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Counterexamples K-Homology and K-Theory Ill Chapter 17 In our final chapter, we present an application of finite-dimensional a ...

432 17. K-Homology fundamental facts, but it is really a bare minimum treatment of the subject (cf. [86]). We will only deal wit ...

17.1. BDF preliminaries 433 Definition 17.1.3. Two essential extensions, 0 -----+ lK ~ £ 1 ~ A -----+ 0 and 0 -----+ lK ~ £2 ~ A ...

434 17. K-Homology Proof. Let 'ljJ: A --+ Q(1i) be a unital *-monomorphism and O": A --+ JIB(JC) be a unital faithful essential ...

17.2. Property (T) and Kazhdan projections 435 In [11] Arveson proved the previous result and simplified the proof of the Choi-E ...

436 17. K-Homology Proof. Taking adjoints and replacing a with a, our intertwining assump- tion also implies n(a)T = TO"(a). Now ...

17.2. Property (T) and Kazhdan projections 437 Definition 17.2.3 (Kazhdan projections). If r has property (T) and the representa ...

438 17. K-Homology Proof. If C'*(I')/J1 had an amenable tracer, then it would also have a finite-dimensional quotient (Remark 6. ...

17.4. Topology on Ext 439 1 7.4. Topology on Ext Finally, we would like to show that noninvertible elements in Ext are often abu ...

440 17. K-Homology Proof. Let (j;: A---+1IB(1i) be a u.c.p. lifting and o-: A-+ 1IB(1i) be a faithful unital essential *-represe ...

References We redefine the pseudometric don Extw(A) by k d([cp], ['lj;]) = i~f L JJucp( vi)u* - 'lj;( vi) JJ. i=l 441 (Not ...

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Part 4 Appendices ...

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