Loading...
Projects / Programmes source: ARIS

Maps on matrices and operators

Research activity

Code Science Field Subfield
1.01.04  Natural sciences and mathematics  Mathematics  Algebra 

Code Science Field
P001  Natural sciences and mathematics  Mathematics 

Code Science Field
1.01  Natural Sciences  Mathematics 
Keywords
matrices, operators, effect algebras, bounded observables, linear and general preservers, geometry of matrices, idempotents and projections
Evaluation (rules)
source: COBISS
Researchers (13)
no. Code Name and surname Research area Role Period No. of publicationsNo. of publications
1.  19551  PhD Dominik Benkovič  Mathematics  Researcher  2017 - 2020  212 
2.  11709  PhD Roman Drnovšek  Mathematics  Researcher  2017 - 2020  270 
3.  19550  PhD Daniel Eremita  Mathematics  Researcher  2017 - 2020  133 
4.  29707  PhD Mateja Grašič  Mathematics  Researcher  2017 - 2020  39 
5.  29584  PhD Marko Kandić  Mathematics  Researcher  2017 - 2020  64 
6.  20037  PhD Marjeta Kramar Fijavž  Mathematics  Researcher  2019 - 2020  185 
7.  30109  PhD Ganna Kudryavtseva  Mathematics  Researcher  2017 - 2020  132 
8.  18893  PhD Bojan Kuzma  Mathematics  Researcher  2017 - 2020  325 
9.  23340  PhD Janko Marovt  Mathematics  Researcher  2017 - 2020  255 
10.  24328  PhD Aljoša Peperko  Mathematics  Researcher  2017 - 2020  197 
11.  33288  PhD Lucijan Plevnik  Mathematics  Researcher  2017 - 2020  24 
12.  05953  PhD Peter Šemrl  Mathematics  Head  2017 - 2020  497 
13.  12191  PhD Aleksej Turnšek  Mathematics  Researcher  2017 - 2020  100 
Organisations (1)
no. Code Research organisation City Registration number No. of publicationsNo. of publications
1.  0101  Institute of Mathematics, Physics and Mechanics  Ljubljana  5055598000  20,258 
Abstract
We will study maps on various operator and matrix algebras and their subsets. In particular, we will be interested in maps defined on: -the algebra of real or complex matrices, -matrix algebras over more general fields or division rings, -the set of idempotent matrices, -the set of projections, -finite-dimensional effect algebras, -the space of hermitian matrices, -the space of alternate matrices, -Minkowski space, and on infinite-dimensional analogues of the above sets, for example: -the algebra of all bounded operators on a Hilbert or a Banach space, -effect algebras on Hilbert spaces, -the set of all idempotent operators (projections), -Jordan algebra of all self-adjoint operators. We will assume that these maps are either linear and have some preserving property (in this case we will speak of linear preserver problems), or they have some preserving properties but we do not assume linearity (in this case we will speak of general preserver problems). It is our aim to describe the general form of such maps.
Significance for science
Our research group publishes in international research journals of high quality. The easiest way to prove the relevance of our research to the development of our scientific field is to check the total citations (according to MathSciNet) of leading researchers Peter Šemrl and Matej Brešar. They were cited 2453 times by 764 authors, and 2733 times by 571 authors, respectively. They have an h-index of 20 and 22, respectively.
Significance for the country
This research grant will support pure mathematics with no direct impact on the economy or the society.
Most important scientific results Interim report, final report
Most important socioeconomically and culturally relevant results Interim report, final report
Views history
Favourite