id,collection,dc.contributor.author,dc.date.accessioned,dc.date.available,dc.date.issued,dc.description.abstract[de],dc.format.extent,dc.identifier.uri,dc.language,dc.relation.ispartofseries,dc.rights.uri,dc.subject,dc.subject.ddc,dc.title,dc.type,dcterms.accessRights.openaire,refubium.affiliation.other,refubium.affiliation[de],refubium.mycore.derivateId,refubium.mycore.fudocsId,refubium.mycore.reportnumber,refubium.series.issueNumber,refubium.series.name,refubium.series.reportNumber "2bfc4ec7-fa53-4155-ae79-52373d037c32","fub188/17741","Hardtke, Jan-David","2018-06-08T07:26:22Z","2014-07-16T08:44:05.830Z","2010","Let X be a real Banach space. A subset B of the dual unit sphere of X is said to be a boundary for X, if every element of X attains its norm on some functional in B. The well-known Boundary Problem originally posed by Godefroy asks whether a bounded subset of X which is compact in the topology of pointwise convergence on B is already weakly compact. This problem was recently solved by Pfitzner in the positive. In this note we collect some stronger versions of the solution to the Boundary Problem, most of which are restricted to special types of Banach spaces. We shall use the results and techniques of Pfitzner, Cascales et al., Moors and others.","15 S.","https://refubium.fu-berlin.de/handle/fub188/17966||http://dx.doi.org/10.17169/refubium-21683","eng","urn:nbn:de:kobv:188-fudocsseries000000000226-9","http://www.fu-berlin.de/sites/refubium/rechtliches/Nutzungsbedingungen","Boundary||weak compactness||convex hull||extreme points||epsilon-weakly relatively compact sets||epsilon-interchangeable double limits","500 Naturwissenschaften und Mathematik::510 Mathematik","Some remarks on stronger versions of the boundary problem for Banach spaces","Preprint","open access","Institut für Mathematik:::bbcc0fd4-8a69-48ba-bf5a-6eae54fc4a88:::600","Mathematik und Informatik","FUDOCS_derivate_000000003711","FUDOCS_document_000000020603","A /13/2010","Preprints, Serie A: Mathematik","Freie Universität Berlin, Fachbereich Mathematik und Informatik","A /13/2010"