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 answer is predicated seriously on suggestions coming from Descriptive Set idea. Thecentralthemeisuniversalityproblems.Inparticular,thetextprovides an exposition of the tools built lately so that it will deal with questions of the next sort: (Q) LetC be a category of separable Banach areas such that each house X within the classC has a definite estate, say estate (P). while do we ?nd a separable Banach house Y which has estate (P) and comprises an isomorphic reproduction of each member ofC? we are going to give some thought to relatively classical homes of Banach areas, resembling “- ing re?exive,” “having separable dual,” “not containing an isomorphic replica of c ,” “being non-universal,” and so forth. zero It seems optimistic solution to challenge (Q), for any of the above pointed out homes, 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 usual “coding” of separable Banach areas, then we will be able to certainly ?nd a separable area 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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