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master's thesis
Normirani i Banachovi prostori
Osijek: Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, 2024. urn:nbn:hr:126:927771
Trojko, Barbara
Josip Juraj Strossmayer University of Osijek
School of Applied Mathematics and Informatics

Institutional repository: Repository of School of Applied Mathematics and Informatics

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Trojko, B. (2024). Normirani i Banachovi prostori (Master's thesis). Osijek: Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics. Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:927771

Trojko, Barbara. "Normirani i Banachovi prostori." Master's thesis, Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, 2024. https://urn.nsk.hr/urn:nbn:hr:126:927771

Trojko, Barbara. "Normirani i Banachovi prostori." Master's thesis, Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, 2024. https://urn.nsk.hr/urn:nbn:hr:126:927771

Trojko, B. (2024). 'Normirani i Banachovi prostori', Master's thesis, Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, accessed 30 November 2024, https://urn.nsk.hr/urn:nbn:hr:126:927771

Trojko B. Normirani i Banachovi prostori [Master's thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics; 2024 [cited 2024 November 30] Available at: https://urn.nsk.hr/urn:nbn:hr:126:927771

B. Trojko, "Normirani i Banachovi prostori", Master's thesis, Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, Osijek, 2024. Available at: https://urn.nsk.hr/urn:nbn:hr:126:927771

Metadata
TitleNormirani i Banachovi prostori
Title (english)Normed And Banach Spaces
AuthorBarbara Trojko
MentorIvan Matić (mentor)
Committee memberJelena Jankov Pavlović (predsjednik povjerenstva)
Committee memberIvan Matić (član povjerenstva)
Committee memberIvana Crnjac (član povjerenstva)
GranterJosip Juraj Strossmayer University of Osijek
School of Applied Mathematics and Informatics
Osijek
Defense date and country2024-10-25, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Other Mathematical Disciplines
Abstract
Normirani vektorski prostori su temelj funkcionalne analize, posebice Banachovi prostori i teorija linearnih operatora unutar njih. Ovaj rad dublje istražuje ove ključne pojmove. Normirani prostori su vektorski prostori opremljeni metrikom koja proizlazi iz norme, što generalizira pojam duljine vektora. Kada normirani prostor također posjeduje potpunost kao metrički prostor, naziva se Banachov prostor. Važno je napomenuti da se svaki normirani prostor može proširiti kako bi postao Banachov prostor. U matematičkim operacijama unutar normiranih prostora, beskonačni nizovi postaju vrijedni alati. Operatori su preslikavanja između normiranih prostora, označena kao X u Y. Ograničeni linearni operatori, koji osiguravaju neprekidnost, posebno su značajni, a temeljni teorem uspostavlja vezu između ograničenosti i neprekidnosti. Prostori operatora su skupovi ograničenih linearnih operatora iz jednog normiranog prostora X u drugi Y, tvoreći sami normirane prostore B(X,Y). U području analize, beskonačnodimenzionalni normirani prostori imaju veći značaj od konačnodimenzionalnih, koji su jednostavniji i omogućuju matrične prikaze operatora.
Abstract (english)
Normed vector spaces are fundamental in functional analysis, particularly Banach spaces and the theory of linear operators within them. This paper delves into these crucial concepts. Normed spaces are vector spaces equipped with a metric derived from a norm, which generalizes the concept of vector length. When a normed space also possesses completeness as a metric space, it’s known as a Banach space. Importantly, any normed space can be extended to form a Banach space. In mathematical operations within normed spaces, infinite series become valuable tools. Operators are mappings between normed spaces, denoted as X to Y. Bounded linear operators, which ensure continuity, are particularly significant, and a fundamental theorem establishes the link between boundedness and continuity. The spaces of operators are collections of bounded linear operators from one normed space X to another Y, forming normed spaces themselves B(X,Y). In the realm of analysis, infinite-dimensional normed spaces hold more prominence than their finite-dimensional counterparts, which are simpler and allow for matrix representations of operators. These concepts serve as the cornerstone of functional analysis.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:927771
Study programmeTitle: Mathematics; specializations in: Financial and Statistical Mathematics, Mathematics and Computer Science, Industrial and Applied Mathematics
Course: Financial and Statistical 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 on2024-10-30 07:37:57