Customized Project N1-0210
Graph Theory in Preserver Problems
Project Title: Graph Theory in Preserver Problems
PI: Bojan Kuzma
Project Code: N1-0210.
Type of the Project: customized project.
Funding Organization: Slovenian Research Agency (ARRS).
Research Field (ARRS): 1.01.00 - Natural Sciences and Mathematics / Mathematics.
Duration: 1. 6. 2021 - 31. 5. 2024.
Project Category: B.
Yearly Range: 0.80 FTE (1.367 research hours).
Sicris profile of the project is here.
- Bojan Kuzma (ARRS code: 18893, PI)
- Vito Vitrih (ARRS code: 27559)
- Slobodan Filipovski (ARRS code: 37715)
- Nina Chiarelli (ARRS code: 35452)
- Orel Marko (ARRS code: 25610)
The proposed project is roughly divided into 4 parts and belongs to the theory of graphs induced by relations and general preservers on:
-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