Use this URL to cite or link to this record in EThOS:  http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.236244 
Title:  A topic in functional analysis  
Author:  Blower, G. 
ISNI:
0000 0001 1692 7220


Awarding Body:  University of Oxford  
Current Institution:  University of Oxford  
Date of Award:  1989  
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Abstract:  
We introduce the class AUMD of Banach spaces X for which Xvalued analytic martingales converge unconditionally. We shew that various possible definitions of this class are equivalent by methods of martingale decomposition. We shew that such X have finite cotype and are qcomplex uniformly convex in the sense of Garling. Using multipliers we shew that analytic martingales valued in L^{1} converge unconditionally and that AUMD spaces have the analytic RadonNikodym property. We shew that X has the AUMD property if and only if strong HbrmanderMihlin multipliers are bounded on the Hardy space H^{1}_{x}(T). We achieve this by representing multipliers as martingale transforms. It is shewn that if X is in AUMD and is of cotype two then X has the Paley Theorem property. Using an isomorphism result we shew that if A is an injective operator system on a separable Hilbert space and P a completely bounded projection on A, then either PA or (IP)A is completely boundedly isomorphic to A. The finitedimensional version of this result is deduced from Ramsey's Theorem. It is shewn that B(e^{2} is primary. It is shewn that weakly compact homomorphisms T from the 2 disc algebra into B(e^{2} are necessarily compact. An explicit form for such T is obtained using spectral projections and it is deduced that such T are absolutely summing.


Supervisor:  Haydon, Richard  Sponsor:  Not available  
Qualification Name:  Thesis (Ph.D.)  Qualification Level:  Doctoral  
EThOS ID:  uk.bl.ethos.236244  DOI:  Not available  
Keywords:  Functional analysis ; Banach spaces ; Martingales (Mathematics)  
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