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master's thesis
Topološke baze normiranih prostora
Zagreb: University of Zagreb, Faculty of Science, 2017. urn:nbn:hr:217:143840
Bobinac, Ivana
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Bobinac, I. (2017). Topološke baze normiranih prostora (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:143840

Bobinac, Ivana. "Topološke baze normiranih prostora." Master's thesis, University of Zagreb, Faculty of Science, 2017. https://urn.nsk.hr/urn:nbn:hr:217:143840

Bobinac, Ivana. "Topološke baze normiranih prostora." Master's thesis, University of Zagreb, Faculty of Science, 2017. https://urn.nsk.hr/urn:nbn:hr:217:143840

Bobinac, I. (2017). 'Topološke baze normiranih prostora', Master's thesis, University of Zagreb, Faculty of Science, accessed 23 December 2024, https://urn.nsk.hr/urn:nbn:hr:217:143840

Bobinac I. Topološke baze normiranih prostora [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2017 [cited 2024 December 23] Available at: https://urn.nsk.hr/urn:nbn:hr:217:143840

I. Bobinac, "Topološke baze normiranih prostora", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2017. Available at: https://urn.nsk.hr/urn:nbn:hr:217:143840

Metadata
TitleTopološke baze normiranih prostora
AuthorIvana Bobinac
MentorDamir Bakić (mentor)
Committee memberDamir Bakić (predsjednik povjerenstva)
Committee memberMaja Resman (član povjerenstva)
Committee memberIlja Gogić (član povjerenstva)
Committee memberIgor Pažanin (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2017-09-26, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
U ovom radu su najprije navedene osnovne definicije i rezultati iz teorije normiranih prostora te su potom izložene osnovne činjenice o bezuvjetnoj konvergenciji redova. U centralnom dijelu rada su prikazani glavni rezultati o topološkim bazama normiranih, odnosno Banachovih prostora. Pokazana je neprekidnost koeficijentnih funkcionala i pokazano je da je svaka baza Banachovog prostora Schauderova baza tog prostora; štoviše, da je ona i slaba baza i slaba Schauderova baza tog prostora. Također su opisani različiti oblici nezavisnosti nizova te su pokazani odnosi među različitim oblicima nezavisnosti. Opisana je biortogonalnost i minimalnost nizova. Posebno, opisane su bezuvjetne baze kao posebno važna klasa topoloških baza. Na kraju su pokazane osnovne činjenice o Rieszovim bazama Hilbertovih prostora.
Abstract (english)
In this thesis, some of the fundamental definitions and results from the theory of normed spaces are first outlined, and then the basic facts about unconditional convergence of series are presented. In the central part of the thesis, the main results about topological bases in normed, that is Banach spaces, are shown. Continuity of coefficient functionals is shown and it is also shown that every basis in a Banach space is Schauder basis in that space, and that it is, in fact, weak basis and weak Schauder basis in that space. Various forms of sequence independence are described and some basic relations among them are shown. Biorthogonality and minimality of sequences are also described. Especially, unconditional bases, which are important class of topological bases, are described. Finally, some basic facts about Riesz bases in Hilbert spaces are shown as well.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:143840
Study programmeTitle: Applied Mathematics
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 on2017-12-18 13:57:14