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

**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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**Extra 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**

Facts about the e s t i m a t e s ence b e t w e e n of our proof esti- Kp < ~81 -. the b o u n d into a Banach surprising estimate. can it is should give b e t t e r an e s t i m a t e and differences. C*-algebra therefore difference gives information somewhat gives than P i s i e r ' s our m e t h o d study b i l i n e a r this a d d i t i o n a l It is t h e r e f o r e a comparison from a the fact that this d e c o m p o s i t i o n based on i n t e r p o l a t i o n better N o w the proofs only involves and since algebras, we finally w a n t to remark the s e l f - a d j o i n t Pisier very c l e a r l y we shall not even that our parts explains state of the the t h e o r e m in that case.

The o p e r a t o r s For a we take a = 3 -½ It is easy to see that 1 -i -i -i 1 -i -i -i 1 T are c o m m u t i n g 3 is d e f i n e d by the same m a t r i x p(z) = so that (p(T) e , f ) = A calculation shows [ j,k aj k contractions. zj z k ~ lajk 12 = 3. j,k that llpll~ < 3. We set out n o w to s h o w that the o b v i o u s example The p o l y n o m i a l generalization satisfies llp(T 1 .... Tj) II <_cjIIPlI. of this 29 where Cj is a constant e n, Inl ~ K depending only on the number J of c o n t r a c - tions.

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. consequence lead has space U is b o u n d e d on ~. norm on ~ Pv while and and The n o r m of Pu Pv the n o r m shall, of all Since the in the that that which, the n o r m an i s o m e t r i c B(H) [7]). of R i n g r o s e , PU as is in fact of the G e l f a n d - N a i m a r k - S e g a l us o u t s i d e It f o l l o w s set subsets ~.