Read e-book online Banach Spaces and Descriptive Set Theory: Selected Topics PDF

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 resolution is predicated seriously on thoughts coming from Descriptive Set idea. Thecentralthemeisuniversalityproblems.Inparticular,thetextprovides an exposition of the tools built lately with the intention to deal with questions of the subsequent sort: (Q) LetC be a category of separable Banach areas such that each area X within the classC has a definite estate, say estate (P). while do we ?nd a separable Banach area Y which has estate (P) and comprises an isomorphic reproduction of each member ofC? we are going to think of relatively classical houses of Banach areas, equivalent to “- ing re?exive,” “having separable dual,” “not containing an isomorphic replica of c ,” “being non-universal,” and so forth. zero It seems confident solution 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 traditional “coding” of separable Banach areas, then we will certainly ?nd a separable house Y that is 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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