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- W1550883301 abstract " We introduce the class AUMD of Banach spaces X for which X -valued 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 q-complex 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 Radon-Nikodym property. We shew that X has the AUMD property if and only if strong Hbrmander-Mihlin 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 ( I-P ) A is completely boundedly isomorphic to A . The finite-dimensional 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." @default.
- W1550883301 created "2016-06-24" @default.
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- W1550883301 date "1989-01-01" @default.
- W1550883301 modified "2023-09-26" @default.
- W1550883301 title "A topic in functional analysis" @default.
- W1550883301 hasPublicationYear "1989" @default.
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