Banach Spaces and Descriptive Set Theory: Selected Topics - download pdf or read online

By Pandelis Dodos

those notes are dedicated to the examine of a few classical difficulties within the Geometry of Banach areas. the newness lies within the indisputable fact that their answer is based seriously on suggestions coming from Descriptive Set thought. Thecentralthemeisuniversalityproblems.Inparticular,thetextprovides an exposition of the tools constructed lately so as to deal with questions of the subsequent variety: (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 will we ?nd a separable Banach house Y which has estate (P) and includes an isomorphic reproduction of each member ofC? we'll contemplate relatively classical houses of Banach areas, comparable to “- ing re?exive,” “having separable dual,” “not containing an isomorphic replica of c ,” “being non-universal,” and so on. zero It seems optimistic resolution to challenge (Q), for any of the above pointed out homes, is feasible if (and primarily provided that) the classC is “simple.” The “simplicity” ofC is measured in set theoretic phrases. accurately, if the classC is analytic in a typical “coding” of separable Banach areas, then we will certainly ?nd a separable area Y that is common for the category C and satis?es the necessities imposed above.

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