By Dale E. Alspach, William B. Johnson (auth.), Ron C. Blei, Stuart J. Sidney (eds.)

ISBN-10: 3540123148

ISBN-13: 9783540123149

ISBN-10: 3540400362

ISBN-13: 9783540400363

**Read or Download Banach Spaces, Harmonic Analysis, and Probability Theory: Proceedings of the Special Year in Analysis, Held at the University of Connecticut 1980–1981 PDF**

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**Additional info for Banach Spaces, Harmonic Analysis, and Probability Theory: Proceedings of the Special Year in Analysis, Held at the University of Connecticut 1980–1981**

**Example text**

B.. i=l 1 1 It follows from t h e o r e m 1 that if jective. and U h is given by the A ~ B, then is an isomorphism, h is sur- so we have to To do this it suffices to prove that for 8 e (~U)', such that ** ~ 0. 48 However, is a g a i n the p r o j e c t i v e a unital algebra. Banach tensor algebra, product so By the B o h n e n b l u s t - K a r l i n ~V of u n i t a l Banach is t h e r e f o r e theorem (lemma algebras a unital 1 above), Banach there ! 11ull CV " It s u f f i c e s S e (~U)' 8S therefore However, defined by to p r o v e S JlBSI 1 = i. **

Let X form on and Y be compact Hausdorff C(X) × C(Y) such that spaces and let I1811 = 8(1,1) = i. 50 Let p be the p r o b a b i l i t y f f dw = 8(f,l). X

C = Ah 8 Bh We shall use the f o l l o w i n g elements to denote in the their definitions. i). finite Let sets V be the {a i } C A h , set of all {b i } C ~ h v = E ai 8 v e C such that such that so t h a t bi and E llaiIl-{ibi{ I ! 1 . 2). finite Let sets U be the {a i } C A h , set of all {bi}C8 h ue C so t h a t u = E ai ® bi and It is c l e a r C and that V C U. e. Pv(W) V U are see that shall n o r m on follows to a t e n s o r that every subalgebra Hilbert space operations given while soon H e.

### Banach Spaces, Harmonic Analysis, and Probability Theory: Proceedings of the Special Year in Analysis, Held at the University of Connecticut 1980–1981 by Dale E. Alspach, William B. Johnson (auth.), Ron C. Blei, Stuart J. Sidney (eds.)

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