| dc.contributor.advisor |
Kečkić, Dragoljub |
|
| dc.contributor.author |
Stefanović, Seđan |
|
| dc.date.accessioned |
2025-04-03T12:38:00Z |
|
| dc.date.available |
2025-04-03T12:38:00Z |
|
| dc.date.issued |
2025-03-25 |
|
| dc.identifier.uri |
http://hdl.handle.net/123456789/5754 |
|
| dc.description.abstract |
The subject of the dissertation is the investigation of the relation of
strong BJ orthogonality in C∗-algebras. For two elements a and b of C∗-algebra
A, we say that a is strong BJ orthogonal to b, if for all c ∈ A holds ‖a + bc‖ ⩾ ‖a‖
and we write a ⊥S b. If it is also true that b ⊥S a, then we say that a and b are
mutual strong BJ orthogonal and write a ⊥⊥S b. To this relation, we associate an
undirected graph Γ(A) (which we call an orthograf), where the vertices are the
nonzero elements of the C∗-algebra A, with the identification of an element and
its scalar multiple; while there is an edge between two vertices a and b if a ⊥⊥S b.
We will show that for any C∗-algebra A, different from three simple
C∗-algebras, and for any two non-isolated vertices a and b in the orthograph,
we can find vertices c1, c2, c3 ∈ Γ(A) such that
a ⊥⊥S c1 ⊥⊥S c2 ⊥⊥S c3 ⊥⊥S b.
We will also describe the isolated vertices of the graph Γ(A) for any C∗-algebra
A. Finally, in the case of finite-dimensional C -algebras, we will determine the
diameter of Γ(A), i.e., the minimum number of elements required to connect any
two vertices. |
en_US |
| dc.description.provenance |
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en |
| dc.description.provenance |
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Previous issue date: 2025-03-25 |
en |
| dc.language.iso |
sr |
en_US |
| dc.publisher |
Beograd |
en_US |
| dc.title |
RELACIJA JAKE VJ ORTOGONALNOSTI NA S - ALGEBRAMA, I OCENE DUŽINE NJENOG GRAFA |
en_US |
| mf.author.birth-date |
1994-06-21 |
|
| mf.author.birth-place |
Šabac |
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 |
Mathematics |
en_US |
| mf.subject.keywords |
C∗-algebras, BJ orthogonality, orthograf, diameter |
en_US |
| mf.subject.subarea |
Functional analysis, Operator algebras |
en_US |
| mf.contributor.committee |
Vujošević, Biljana |
|
| mf.contributor.committee |
Lazović, Zlatko |
|
| mf.contributor.committee |
Kuzma, Bojan |
|
| mf.university.faculty |
Mathematical Faculty |
en_US |
| mf.document.references |
86 |
en_US |
| mf.document.pages |
141 |
en_US |
| mf.document.location |
Beograd |
en_US |
| mf.document.genealogy-project |
No |
en_US |
| mf.university |
Belgrade University |
en_US |