POLU-FREDHOLMOVI OPERATORI NA HILBERTOVIM C*-MODULIMA

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POLU-FREDHOLMOVI OPERATORI NA HILBERTOVIM C*-MODULIMA

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dc.contributor.advisor Đorđević, Dragan
dc.contributor.author Ivković, Stefan
dc.date.accessioned 2021-11-29T18:47:59Z
dc.date.available 2021-11-29T18:47:59Z
dc.date.issued 2021
dc.identifier.uri http://hdl.handle.net/123456789/5305
dc.description.abstract In the first part of the thesis, we establish the semi-Fredholm theory on Hilbert C∗- modules as a continuation of the Fredholm theory on Hilbert C∗-modules which was introduced by Mishchenko and Fomenko. Starting from their definition of C∗-Fredholm operator, we give definition of semi-C∗-Fredholm operator and prove that these operators correspond to one-sided invertible elements in the Calkin algebra. Also, we give definition of semi-C∗-Weyl operators and semi-C∗-B-Fredholm operators and obtain in this connection several results generalizing the counterparts from the classical semi-Fredholm theory on Hilbert spaces. Finally, we consider closed range operators on Hilbert C∗-modules and give necessary and sufficient conditions for a composition of two closed range C∗-operators to have closed image. The second part of the thesis is devoted to the generalized spectral theory of operators on Hilbert C∗-modules. We introduce generalized spectra in C∗-algebras of C∗-operators and give description of such spectra of shift operators, unitary, self-adjoint and normal operators on the standard Hilbert C∗- module. Then we proceed further by studying generalized Fredholm spectra (in C∗-algebras) of operators on Hilbert C∗-modules induced by various subclasses of semi-C∗-Fredholm operators. In this setting we obtain generalizations of some of the results from the classical spectral semi-Fredholm theory such as the results by Zemanek regarding the relationship between the spectra of an operator and the spectra of its compressions. Also, we study 2×2 upper triangular operator matrices acting on the direct sum of two standard Hilbert C∗-modules and describe the relationship between semi-C∗-Fredholmness of these matrices and of their diagonal entries. en_US
dc.description.provenance Submitted by Slavisha Milisavljevic (slavisha) on 2021-11-29T18:47:59Z No. of bitstreams: 1 Stefan_Ivkovic_Doktorska_disertacija.pdf: 1505601 bytes, checksum: 0ff9dc5611eb9ed483b8c416a39d65f0 (MD5) en
dc.description.provenance Made available in DSpace on 2021-11-29T18:47:59Z (GMT). No. of bitstreams: 1 Stefan_Ivkovic_Doktorska_disertacija.pdf: 1505601 bytes, checksum: 0ff9dc5611eb9ed483b8c416a39d65f0 (MD5) Previous issue date: 2021 en
dc.language.iso sr en_US
dc.publisher Beograd en_US
dc.title POLU-FREDHOLMOVI OPERATORI NA HILBERTOVIM C*-MODULIMA en_US
mf.author.birth-date 1989-08-03
mf.author.birth-place Jagodina en_US
mf.author.birth-country Srbija en_US
mf.author.residence-state Srbija en_US
mf.author.citizenship Srpsko en_US
mf.author.nationality Srbin en_US
mf.subject.area MA en_US
mf.subject.keywords Hilbert C∗-module, semi-C∗-Fredholm operator, semi-C∗-Weyl operator, semi-C∗- B-Fredholm operator, essential spectrum, Weyl spectrum, perturbation of spectra, compression en_US
mf.subject.subarea Analysis, operator theory and operator algebra en_US
mf.contributor.committee Frank, Mikael
mf.contributor.committee Manuilov, Vladimir
mf.contributor.committee Trapani, Kamilo
mf.contributor.committee Troicki, Jevgenij
mf.contributor.committee Živković Zlatanović, Snežana
mf.contributor.committee Jocić, Danko
mf.document.references 56 en_US
mf.document.pages 152 en_US
mf.document.location Beograd en_US
mf.document.genealogy-project No en_US
mf.university Belgrade University en_US

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