Projects / Programmes
Maps on matrices and operators
| 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 |
matrices, operators, effect algebras, bounded observables, linear and general preservers,
geometry of matrices, idempotents and projections
Researchers (13)
Organisations (1)
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
