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Projects / Programmes source: ARRS

Maps on matrices and operators

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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
Citations Citations for bibliographic records in COBIB.SI that are linked to records in citation databases
source: WoS source: Scopus source: COBISS
Researchers (13)
no. Code Name and surname Research area Role Period No. of publications
1.  19551  PhD Dominik Benkovič  Natural sciences and mathematics  Researcher  2017 - 2020  206 
2.  11709  PhD Roman Drnovšek  Natural sciences and mathematics  Researcher  2017 - 2020  266 
3.  19550  PhD Daniel Eremita  Natural sciences and mathematics  Researcher  2017 - 2020  129 
4.  29707  PhD Mateja Grašič  Natural sciences and mathematics  Researcher  2017 - 2020  38 
5.  29584  PhD Marko Kandić  Natural sciences and mathematics  Researcher  2017 - 2020  62 
6.  20037  PhD Marjeta Kramar Fijavž  Natural sciences and mathematics  Researcher  2019 - 2020  177 
7.  30109  PhD Ganna Kudryavtseva  Natural sciences and mathematics  Researcher  2017 - 2020  124 
8.  18893  PhD Bojan Kuzma  Natural sciences and mathematics  Researcher  2017 - 2020  313 
9.  23340  PhD Janko Marovt  Natural sciences and mathematics  Researcher  2017 - 2020  245 
10.  24328  PhD Aljoša Peperko  Natural sciences and mathematics  Researcher  2017 - 2020  186 
11.  33288  PhD Lucijan Plevnik  Natural sciences and mathematics  Researcher  2017 - 2020  23 
12.  05953  PhD Peter Šemrl  Natural sciences and mathematics  Principal Researcher  2017 - 2020  488 
13.  12191  PhD Aleksej Turnšek  Natural sciences and mathematics  Researcher  2017 - 2020  100 
Organisations (1)
no. Code Research organisation City Registration number No. of publications
1.  0101  Institute of Mathematics, Physics and Mechanics  Ljubljana  5055598000  19,695 
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
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