New PDF release: Banach Spaces and Descriptive Set Theory: Selected Topics

By Pandelis Dodos

those notes are dedicated to the research of a few classical difficulties within the Geometry of Banach areas. the newness lies within the undeniable fact that their resolution is based seriously on ideas coming from Descriptive Set thought. Thecentralthemeisuniversalityproblems.Inparticular,thetextprovides an exposition of the equipment built lately so that it will deal with questions of the next kind: (Q) LetC be a category of separable Banach areas such that each house X within the classC has a definite estate, say estate (P). whilst do we ?nd a separable Banach area Y which has estate (P) and includes an isomorphic replica of each member ofC? we are going to examine fairly classical homes of Banach areas, comparable to “- ing re?exive,” “having separable dual,” “not containing an isomorphic reproduction of c ,” “being non-universal,” and so on. zero It seems optimistic resolution to challenge (Q), for any of the above pointed out houses, is feasible if (and basically provided that) the classC is “simple.” The “simplicity” ofC is measured in set theoretic phrases. accurately, if the classC is analytic in a ordinary “coding” of separable Banach areas, then we will certainly ?nd a separable house Y that's common for the category C and satis?es the necessities imposed above.

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Banach Spaces and Descriptive Set Theory: Selected Topics (Lecture Notes in Mathematics) by Pandelis Dodos

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