| 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
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en |
| dc.description.provenance |
Made available in DSpace on 2021-11-29T18:47:59Z (GMT). No. of bitstreams: 1
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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 |