Ortogonalnost u normiranim prostorima

master's thesis

• Author: Mihael Končić
• Mentor: Tomislav Berić (mentor)
• Committee member: Tomislav Berić (predsjednik povjerenstva)
• Committee member: Boris Guljaš (član povjerenstva)
• Committee member: Damir Bakić (član povjerenstva)
• Committee member: Igor Ciganović (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2019-09-26, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U ovom diplomskom radu bavili smo se pitanjem poopćenja ortogonalnosti na normirane prostore u kojima općenito ne postoji skalarni produkt. Za početak smo definirali osnovne pojmove vezane za unitarne i normirane prostore te vezu između njih. Također smo uveli šest svojstava koje klasična ortogonalnost zadovoljava na unitarnom prostoru. U drugom poglavlju navodimo različite definicije poopćenja ortogonalnosti u normiranim prostorima. Svako od tih poopćenja smo posebno komentirali, pokazali da se zaista radi o poopćenju te provjerili koja od šest svojstva ortogonalnosti su zadovoljena. U posljednjem poglavlju bavili smo se pitanjem koliko je neki normiran prostor daleko od toga da bude unitaran, stoga smo uveli neke konstante kojima možemo mjeriti ta odstupanja.

Abstract (english)

In this graduate thesis we discussed the problem of generalised orthogonalities in normed spaces where an inner product may not exist. Firstly we introduced basic definitions related to inner product and normed spaces as well as the connection between the two. We have also introduced six properties which the classical definition of orthogonality in inner product spaces satisfies. In second chapter various definitions of generalized orthogonality in normed spaces were introduced. We debated each one of these orthogonalities separately, proved that they really are generalised orthogonalities and we also checked which orthogonality properties they satisfy. In the last chapter we discussed how close is a normed space to being a Hilbert space. To that end some constants which measure those deviations were introduced.

• Keywords: ortogonalnost; normirani prostori; poopćenje ortogonalnosti
• Keywords (english): orthogonality; normed spaces; generalised orthogonalities
• Language: croatian
• URN:NBN: urn:nbn:hr:217:465053
• Study programme: Title: Applied 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: 2020-02-06 11:13:29