Topološke baze Banachovih prostora

master's thesis

• Author: Hrvoje Stojanović
• Mentor: Damir Bakić (mentor)
• Committee member: Damir Bakić (predsjednik povjerenstva)
• Committee member: Zvonko Čerin (član povjerenstva)
• Committee member: Igor Pažanin (član povjerenstva)
• Committee member: Goran Igaly (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2015-07-10, 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: topološke bazae na Banachovim prostorima; Hahn-Banachov teorem; princip uniformne ograničenosti; bezuvjetne baze
• Keywords (english): topological bases in Banach spaces; Hahn-Banach theorem; uniform boundedness theorem; unconditional bases
• Language: croatian
• URN:NBN: urn:nbn:hr:217:540038
• Study programme: Title: Pure Mathematics; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2019-02-07 13:42:42