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master's thesis
Bezuvjetne baze Banachovih prostora
Zagreb: University of Zagreb, Faculty of Science, 2021. urn:nbn:hr:217:245556
Ban, Matko
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Ban, M. (2021). Bezuvjetne baze Banachovih prostora (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:245556

Ban, Matko. "Bezuvjetne baze Banachovih prostora." Master's thesis, University of Zagreb, Faculty of Science, 2021. https://urn.nsk.hr/urn:nbn:hr:217:245556

Ban, Matko. "Bezuvjetne baze Banachovih prostora." Master's thesis, University of Zagreb, Faculty of Science, 2021. https://urn.nsk.hr/urn:nbn:hr:217:245556

Ban, M. (2021). 'Bezuvjetne baze Banachovih prostora', Master's thesis, University of Zagreb, Faculty of Science, accessed 03 April 2025, https://urn.nsk.hr/urn:nbn:hr:217:245556

Ban M. Bezuvjetne baze Banachovih prostora [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2021 [cited 2025 April 03] Available at: https://urn.nsk.hr/urn:nbn:hr:217:245556

M. Ban, "Bezuvjetne baze Banachovih prostora", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2021. Available at: https://urn.nsk.hr/urn:nbn:hr:217:245556

Metadata
TitleBezuvjetne baze Banachovih prostora
Title (english)Unconditional bases of Banach spaces
AuthorMatko Ban
MentorDamir Bakić (mentor)
Committee memberDamir Bakić (predsjednik povjerenstva)
Committee memberMarcela Hanzer (član povjerenstva)
Committee memberVjekoslav Kovač (član povjerenstva)
Committee memberEduard Marušić-Paloka (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2021-07-22, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
U ovome radu cilj nam je bio proučiti i opisati osnovna svojstva bezuvjetnih baza. U prvome poglavlju smo uveli rezultate iz raznih područja koji su nam bili potrebni za opis problema. U drugom poglavlju smo opisali baze na Banachovim prostorima i njihova svojstva, počevši od Hamelovih baza, s kojima smo se prije susreli u konačnodimenzionalnim prostorima. Definirali smo i opisali neke vrste baza (bezuvjetne, apsolutno konvergentne, ograničene i normalizirane baze), detaljnije smo proučili... More Schauderove baze, te smo opisali i proučili svojstvo ekvivalencije baza u beskonačnodimenzionalnim Banachovim prostorima. Također, proučili smo i trigonometrijski sustav, {e2πint}n∈Z. U trećem poglavlju pozabavili smo se svojstvima baza: definicijom, svojstvima minimalnosti i biortogonalnosti, te karakterizacijom Schauderovih baza i minimalnih nizova. Također smo se pozabavili pitanjem nezavisnosti u beskonačnodimenzionalnim prostorima. U zadnjem poglavlju smo opisali bezuvjetne baze. Proučili smo njihova osnovna svojstva i karakterizaciju, uveli pojam bezuvjetne bazne konstante i naučili kako ju najbolje odrediti, te smo uvidjeli da Schauderov sustav ne može biti bezuvjetan. Less
Abstract (english)
In this paper, our goal was to analyze and describe the properties of unconditional bases. In the first chapter, we’ve introduced the results we needed to describe the problem. In the second chapter, we have defined the bases on Banach spaces and described their properties, starting with Hamel bases, which we referred to as bases in finite dimensional spaces. We have defined and described several types of bases (such as the unconditional bases, absolutely convergent bases, bounded bases,... More and normalized bases), we studied Schauder bases in detail, and have described equivalence of bases in infinite dimensional Banach spaces. Also, we’ve described the trigonometric system, {e2πint}n∈Z. In the third chapter, we had a closer look at basis properties: definition, minimality, biorthogonality, and independence when in infinite dimensional Banach spaces. We’ve characterized Schauder bases and minimal sequences and found out how minimality and Schauder bases are related.. In the last chapter, we’ve described the unconditional bases. We characterized them, described their basic properties, introduced the definition of unconditional basis constant (its properties, and how to find it). At last, we’ve shown that the Schauder system cannot be unconditional. Less
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:245556
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 on2021-09-14 08:41:33
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