Please use this identifier to cite or link to this item: http://hdl.handle.net/10525/487

 Title: Compactness in the First Baire Class and Baire-1 Operators Authors: Mercourakis, S.Stamati, E. Keywords: Baire-1 FunctionBaire-1 OperatorRosenthal CompactRosenthal-Banach CompactPolish SpaceAngelic SpaceBounded Approximation Property Issue Date: 2002 Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences Citation: Serdica Mathematical Journal, Vol. 28, No 1, (2002), 1p-36p Abstract: For a polish space M and a Banach space E let B1 (M, E) be the space of first Baire class functions from M to E, endowed with the pointwise weak topology. We study the compact subsets of B1 (M, E) and show that the fundamental results proved by Rosenthal, Bourgain, Fremlin, Talagrand and Godefroy, in case E = R, also hold true in the general case. For instance: a subset of B1 (M, E) is compact iff it is sequentially (resp. countably) compact, the convex hull of a compact bounded subset of B1 (M, E) is relatively compact, etc. We also show that our class includes Gulko compact. In the second part of the paper we examine under which conditions a bounded linear operator T : X ∗ → Y so that T |BX ∗ : (BX ∗ , w∗ ) → Y is a Baire-1 function, is a pointwise limit of a sequence (Tn ) of operators with T |BX ∗ : (BX ∗ , w∗ ) → (Y, · ) continuous for all n ∈ N. Our results in this case are connected with classical results of Choquet, Odell and Rosenthal. URI: http://hdl.handle.net/10525/487 ISSN: 1310-6600 Appears in Collections: Volume 28 Number 1

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