Uporaba grafov v problemih ohranjevalcev / Graph Theory in Preserver Problems
natisniNaslov projekta:
Uporaba grafov v problemih ohranjevalcev / Graph Theory in Preserver Problems
N1-0210
UP FAMNIT
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Financer projekta:
Javna agencija RS za raziskovalno dejavnost (ARRS)
Prilagojeni raziskovalni projekt
1.01. - Naravoslovno-matematične vede
1. 6. 2021 - 31. 05. 2024
Predlagani projekt je v grobem razdeljen na 4 dele in raziskuje grafe, inducirane z relacijami ter splošne ohranjevalce na
-normiranih prostorih,
-Hilbertovih C*-modulih,
-matričnih algebrah,
-množicah (ne nujno zveznih) operatorjev, in
-mnogoterostmi povezanimi s specialno teorijo relativnosti.
Bolj natančno, znotraj predlaganega projekta nameravamo:
(1) Preučevati lastnosti grafov, ki jih inducirajo Birkhoff-Jamesova ortogonalnost, Robertsova ortogonalnost ter močna Birkhoff-Jamesova ortogonalnost, in klasificirati njihove (linearne) ohranjevalce.
(2) Klasificirati splošne bijektivne bi-ohranjevalce leve-zvezdica urejenosti na B(H).
(3) Klasificirati aditivne preslikave, ki ohranijo spekter neomejenih linearnih operatorjev na kompleksnih Banachovih prostorih.
(4) Klasificirati preslikave na de Sitter-jevem prostoru, ki geodetke svetlobnega tipa slikajo zopet v geodetke svetlobnega tipa. Injektivnost tovrstnih preslikav bomo privzeli le na vsaki svetlobni geodetki posebej. The proposed project is roughly divided into 4 parts and belongs to the theory of graphs induced by relations and general preservers on:
-Hilbert C*-modules,
-sets of (possibly unbounded) operators, and
-manifolds related to special relativity.
In particular we aim to:
(1) Study the properties of graph induced by Birkhoff-James and Roberts orthogonality and also induced by strong Birkhoff-James orthogonality and study their (linear) preservers.
(2) Classify general bijective bi-preservers of left-star partial order on B(H).
(3) Classify additive maps which preserve the spectrum of unbounded linear operators on a complex Banach space.
(4) Classify maps on the de Sitter space, which maps light-like geodesics into light-like geodesics. Injectivity of the maps will be assumed only on each light-like geodesic separately
-normiranih prostorih,
-Hilbertovih C*-modulih,
-matričnih algebrah,
-množicah (ne nujno zveznih) operatorjev, in
-mnogoterostmi povezanimi s specialno teorijo relativnosti.
Bolj natančno, znotraj predlaganega projekta nameravamo:
(1) Preučevati lastnosti grafov, ki jih inducirajo Birkhoff-Jamesova ortogonalnost, Robertsova ortogonalnost ter močna Birkhoff-Jamesova ortogonalnost, in klasificirati njihove (linearne) ohranjevalce.
(2) Klasificirati splošne bijektivne bi-ohranjevalce leve-zvezdica urejenosti na B(H).
(3) Klasificirati aditivne preslikave, ki ohranijo spekter neomejenih linearnih operatorjev na kompleksnih Banachovih prostorih.
(4) Klasificirati preslikave na de Sitter-jevem prostoru, ki geodetke svetlobnega tipa slikajo zopet v geodetke svetlobnega tipa. Injektivnost tovrstnih preslikav bomo privzeli le na vsaki svetlobni geodetki posebej. The proposed project is roughly divided into 4 parts and belongs to the theory of graphs induced by relations and general preservers on:
-Hilbert C*-modules,
-sets of (possibly unbounded) operators, and
-manifolds related to special relativity.
In particular we aim to:
(1) Study the properties of graph induced by Birkhoff-James and Roberts orthogonality and also induced by strong Birkhoff-James orthogonality and study their (linear) preservers.
(2) Classify general bijective bi-preservers of left-star partial order on B(H).
(3) Classify additive maps which preserve the spectrum of unbounded linear operators on a complex Banach space.
(4) Classify maps on the de Sitter space, which maps light-like geodesics into light-like geodesics. Injectivity of the maps will be assumed only on each light-like geodesic separately
Oddelek za matematiko
