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National Repository of Grey Literature 21 records found  beginprevious21 - 21  jump to record: Search took 0.00 seconds. 
Descriptive properties of sets in Banach spaces
 Kurka, Ondřej ; Zajíček, Luděk (referee) ; Holický, Petr (advisor)
An essential part of the work is devoted to the study of the sets of Fréchet subdi erentiability from the view of the descriptive set theory. Proofs of the known results of L. Zajíek, P. Holický, M. Laczkovich and M. Šmídek are given. A new result is that there exists a Lipschitz function with non-Borel set of Fréchet subdi erentiability on every non-reflexive Banach space. The Borel classes of the sets of Fréchet subdi erentiability of continuous functions on reflexive spaces are studied as well. Further, some sets of sequences in Banach spaces are investigated. A modi ed proof of the theorem of R. Kaufman which says that every non-re exive Banach space can be renormed not to have Borel set of norm-attaining functionals is shown. A characterization of non-quasire exive Banach spaces is given.
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