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.

Research Organization:

University of Primorska, UP FAMNIT

Project Members:

• 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)

Abstract:

The proposed project is roughly divided into 4 parts and belongs to the theory of graphs induced by relations and general preservers on:

-normed spaces,

-Hilbert C*-modules,

-matrix algebras, 

-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