Embeddings and factorizations of Banach spaces

dc.contributorJohnson, William B.
dc.creatorZheng, Bentuo
dc.date.accessioned2010-01-14T23:58:01Z
dc.date.accessioned2010-01-16T01:54:39Z
dc.date.accessioned2017-04-07T19:56:31Z
dc.date.available2010-01-14T23:58:01Z
dc.date.available2010-01-16T01:54:39Z
dc.date.available2017-04-07T19:56:31Z
dc.date.created2007-08
dc.date.issued2009-05-15
dc.description.abstractOne problem, considered important in Banach space theory since at least the 1970?s, asks for intrinsic characterizations of subspaces of a Banach space with an unconditional basis. A more general question is to give necessary and sufficient conditions for operators from Lp (2 < p < 1) to factor through `p. In this dissertaion, solutions for the above problems are provided. More precisely, I prove that for a reflexive Banach space, being a subspace of a reflexive space with an unconditional basis or being a quotient of such a space, is equivalent to having the unconditional tree property. I also show that a bounded linear operator from Lp (2 < p < 1) factors through `p if and only it satisfies an upper-(C, p)-tree estimate. Results are then extended to operators from asymptotic lp spaces.
dc.identifier.urihttp://hdl.handle.net/1969.1/ETD-TAMU-1551
dc.language.isoen_US
dc.subjectembeddings
dc.subjectfactorizations
dc.titleEmbeddings and factorizations of Banach spaces
dc.typeBook
dc.typeThesis

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