Banach Spaces, Harmonic Analysis, and Probability Theory: - download pdf or read online

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

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Read Online 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 resources 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

Introduction The p u r p o s e theorem of this p a p e r for b i l i n e a r a commutative "fundamental theorem is to give forms on a C*-algebra, theorem" is t h e r e f o r e C*-algebra. Pisier's on tensor products. seems to be a very explains It also of Lq(~,P) and the simple seems to be quite theorem (q > 2, L2-norm C(X)-space Grothendieck's of this theorem theorem. illuminating are equivalent, measure) then every it p r o o f of that in the sense In one way or a n o t h e r a probability and we be- If so, are based on the fact that if P is Our n e w p r o o f of P i s i e r ' s (not to say simple-minded) why other proofs work.

F = 3 n fn-]l 3 = 0 < shift Ek K-I on " Fk if n. > 0 3 if n = 0. 3 As an intermediary S: EK + F K. Let consider it h a v e FK matrix Seq Then on backwards EK and we define Tj: shift FK ÷ FK_ I. s(p,q) us d e n o t e a contraction that s(p,q) sj(p,q) EK ÷ FK-I o by = s(p+lj, q), Tj p ~ /K-I' s. 3 is the q) fp iff is d e f i n e d the so t h a t ~ s(p+~j, s(p,q) Here S : [ s(p,q) fp . Tjeq Let define = 0(p+q). q £ IK" amounts Clearly to the Tj fact is 30 Lemma. llSIlop ! jl/2 . Proof. Let b e £2(I K) llsjlIo p < i, and let a(p) IIajli < IIbil w h e r e [ aj(p) J [ la(P)[ 2 < pel K and the r e s u l t = Z s(p,q)b(q).

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.

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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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