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master's thesis
Topološke baze Banachovih prostora
Zagreb: University of Zagreb, Faculty of Science, 2015. urn:nbn:hr:217:540038
Stojanović, Hrvoje
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Stojanović, H. (2015). Topološke baze Banachovih prostora (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:540038

Stojanović, Hrvoje. "Topološke baze Banachovih prostora." Master's thesis, University of Zagreb, Faculty of Science, 2015. https://urn.nsk.hr/urn:nbn:hr:217:540038

Stojanović, Hrvoje. "Topološke baze Banachovih prostora." Master's thesis, University of Zagreb, Faculty of Science, 2015. https://urn.nsk.hr/urn:nbn:hr:217:540038

Stojanović, H. (2015). 'Topološke baze Banachovih prostora', Master's thesis, University of Zagreb, Faculty of Science, accessed 23 December 2024, https://urn.nsk.hr/urn:nbn:hr:217:540038

Stojanović H. Topološke baze Banachovih prostora [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2015 [cited 2024 December 23] Available at: https://urn.nsk.hr/urn:nbn:hr:217:540038

H. Stojanović, "Topološke baze Banachovih prostora", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2015. Available at: https://urn.nsk.hr/urn:nbn:hr:217:540038

Metadata
TitleTopološke baze Banachovih prostora
AuthorHrvoje Stojanović
MentorDamir Bakić (mentor)
Committee memberDamir Bakić (predsjednik povjerenstva)
Committee memberZvonko Čerin (član povjerenstva)
Committee memberIgor Pažanin (član povjerenstva)
Committee memberGoran Igaly (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2015-07-10, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
U ovome radu su izloženi neki temeljni rezultati o topološkim bazama na Banachovim prostorima. Glavni alati koji se pritom koriste su osnovni rezultati iz teorije normiranih prostora poput Hahn-Banachovog teorema i principa uniformne ograničenosti. Ključno pokazano svojstvo topoloških baza je neprekidnost koeficijenata iz zapisa vektora preko baze (s obzirom na te vektore). Opisane su veze između topoloških baza i njima po svojstvima sličnih nizova. Posebno je opisana jedna posebna klasa topoloških baza: bezuvjetne baze za koje konvergencija ne ovisi o poretku elemenata baze.
Abstract (english)
In this thesis we have presented some fundamental results about topological bases in Banach spaces. Main tools used for that are fundamental results from theory of normed spaces such as Hahn-Banach theorem and uniform boundedness theorem. We have presented key property of topological bases which states that the coefficients from basis representations of vectors are continuous (with respect to those vectors). We have described some relations between topological bases and some other types of sequences that are similar to topological bases. In the end one special class of topological bases was described: unconditional bases for which convergence doesn’t depend on the ordering of the elements in the basis.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:540038
Study programmeTitle: Pure 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 on2019-02-07 13:42:42