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master's thesis
Geometrijska svojstva UMD prostora
Zagreb: University of Zagreb, Faculty of Science, 2020. urn:nbn:hr:217:619683
Depope, Al
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

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Depope, A. (2020). Geometrijska svojstva UMD prostora (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:619683

Depope, Al. "Geometrijska svojstva UMD prostora." Master's thesis, University of Zagreb, Faculty of Science, 2020. https://urn.nsk.hr/urn:nbn:hr:217:619683

Depope, Al. "Geometrijska svojstva UMD prostora." Master's thesis, University of Zagreb, Faculty of Science, 2020. https://urn.nsk.hr/urn:nbn:hr:217:619683

Depope, A. (2020). 'Geometrijska svojstva UMD prostora', Master's thesis, University of Zagreb, Faculty of Science, accessed 13 June 2024, https://urn.nsk.hr/urn:nbn:hr:217:619683

Depope A. Geometrijska svojstva UMD prostora [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2020 [cited 2024 June 13] Available at: https://urn.nsk.hr/urn:nbn:hr:217:619683

A. Depope, "Geometrijska svojstva UMD prostora", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2020. Available at: https://urn.nsk.hr/urn:nbn:hr:217:619683

Metadata
TitleGeometrijska svojstva UMD prostora
AuthorAl Depope
MentorZoran Vondraček (mentor)
Committee memberZoran Vondraček (predsjednik povjerenstva)
Committee memberVjekoslav Kovač (član povjerenstva)
Committee memberRudi Mrazović (član povjerenstva)
Committee memberMiljenko Huzak (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2020-09-29, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
U diplomskom radu bavimo se Banachovim prostorima s UMD (engl. unconditional martingale difference) svojstvom. Riječ je o vjerojatnosnom svojstvu s važnim implikacijama u harmonijskog analizi i teoriji Banachovih prostora. U uvodnom je dijelu rada dan kratki pregled teorije integracije u Banachovim prostorima te dokazana Jamesova karakterizacija refleksivnosti Banachovih prostora (Teorem 1.2.15). U središnjem dijelu dokazujemo da UMD svojstvo povlači super-refleksivnost pripadnog Banachovog prostora (Propozicija 2.2.7) te prezentiramo Burkholderovu geometrijsku karakterizaciju Banachovih prostora s UMD svojstvom u terminima \(\zeta\)-konveksnosti (Teorem 3.1.12).
Abstract (english)
This master’s thesis studies Banach spaces with the UMD (unconditional martingale difference) property. Although the UMD property is defined probabilistically, it is known that it has important implications in harmonic analysis as well as in Banach space theory. In the introductory part we give an overview of the integration theory in Banach spaces. We also prove James’s characterization of reflexivity of Banach spaces. (Theorem 1.2.15). In the main part of the thesis we prove that the UMD property implies super-reflexivity (Proposition 2.2.7) and we present Burkholder’s geometric characterization of the UMD property in terms of \(\zeta\)-convexity (Theorem 3.1.12).
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:619683
Study programmeTitle: Mathematical Statistics
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2020-12-08 11:31:22