# Topics in Modern Operator Theory: 5.Intern.Conference by Constantin, Douglas, Nagy, Voiculescu

By Constantin, Douglas, Nagy, Voiculescu

**Read Online or Download Topics in Modern Operator Theory: 5.Intern.Conference Operator Theory,Timisoara,Herculana,1980 (Operator Theory: Advances and Applications) PDF**

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**Additional resources for Topics in Modern Operator Theory: 5.Intern.Conference Operator Theory,Timisoara,Herculana,1980 (Operator Theory: Advances and Applications)**

**Example text**

In fact these three norms are equal. To see this it is convenient to introduce a fourth norm on A. ,Pn) is a D-partition). It is easy to see that the right hand side above defines a semi- norm on B(H)s. Moreover, by Lemma 1 its null space is precisely J so that is a well-defined norm on A. PROPOSITION 4. 112 ane equal. PROOF. ,PnI is a D-partition, then as shown in the proof of Lemma 1, A-EP iAPieJ for A in B(H)s. ,Pn). Hence, To show fix a in A, a>O and write A=11a112. Select A and B in B(H) s such that u(A)=u(B)=a and -(A+e)15A 5(A+e)1.

Moreover, if (T) is a representation for an element a in Ext (X), then a in Ext (X) corresponds to (ind (T-ai))i-1 where li is a point in Oi. THEOREM. The element a to Ext (X) ti4 C1-4mooth £ and only tj LIind (T-Ai)Iarea (Oi)

Hence, 37 ANDERSON -(X+e)PiSPiAPiSPiBPi+cP1S(X+2c)Pi for 15i:5n so that IIEPiAPiII5a+2c and therefore Hall p511a112. to complete the proof it only remains to Since Fix a in A and choose A in B(H) s such that show u(A)=a and Hall q+c-IIAII. Since -IIAI{15ASIIAII1, -(Ilallq+c)e5 Sa5(Ilallq+c)e and I1all1:5Ilallq . Since j is uniformly Let us denote the norm on A by (A,j,e) is a complete order unit closed and space. 81 A is iso- metrically and order isomorphic to A(K), the continuous affine functions on the state space K of A.