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Projects / Programmes source: ARIS

Applications of algebra in analysis

Research activity

Code Science Field Subfield
1.01.00  Natural sciences and mathematics  Mathematics   

Code Science Field
P120  Natural sciences and mathematics  Number theory, field theory, algebraic geometry, algebra, group theory 
P140  Natural sciences and mathematics  Series, Fourier analysis, functional analysis 
Keywords
functional analysis, operator theory, algebra, multiparameter spectral analysis, invariant subspaces, semigroups, groups, matrix varieties
Evaluation (rules)
source: COBISS
Researchers (19)
no. Code Name and surname Research area Role Period No. of publicationsNo. of publications
1.  12040  PhD Janez Bernik  Mathematics  Researcher  2004 - 2007  120 
2.  19511  PhD Janko Bračič  Mathematics  Researcher  2004 - 2007  353 
3.  19250  PhD Anita Buckley  Mathematics  Researcher  2004 - 2007  39 
4.  13430  PhD Gregor Cigler  Mathematics  Researcher  2004 - 2007  61 
5.  15127  PhD Jakob Cimprič  Mathematics  Researcher  2004 - 2007  85 
6.  16331  PhD David Dolžan  Mathematics  Researcher  2004 - 2007  139 
7.  11709  PhD Roman Drnovšek  Mathematics  Researcher  2004 - 2007  271 
8.  03429  PhD Milan Hladnik  Mathematics  Researcher  2004 - 2007  218 
9.  12190  PhD Damjana Kokol Bukovšek  Mathematics  Researcher  2004 - 2007  155 
10.  08398  PhD Tomaž Košir  Mathematics  Researcher  2004 - 2007  429 
11.  20037  PhD Marjeta Kramar Fijavž  Mathematics  Researcher  2004 - 2007  185 
12.  18893  PhD Bojan Kuzma  Mathematics  Researcher  2004 - 2007  325 
13.  24184  PhD Nika Novak  Mathematics  Researcher  2004 - 2007  22 
14.  09573  PhD Matjaž Omladič  Mathematics  Head  2004 - 2007  452 
15.  18838  PhD Primož Potočnik  Mathematics  Researcher  2004 - 2007  239 
16.  19601  MSc Katarina Šenk  Mathematics  Researcher  2004 - 2007  48 
17.  12191  PhD Aleksej Turnšek  Mathematics  Researcher  2004 - 2007  100 
18.  23962  PhD Dejan Velušček  Energy engineering  Researcher  2004 - 2007  52 
19.  16201  PhD Bojana Zalar  Mathematics  Researcher  2004 - 2007  16 
Organisations (1)
no. Code Research organisation City Registration number No. of publicationsNo. of publications
1.  0101  Institute of Mathematics, Physics and Mechanics  Ljubljana  5055598000  20,138 
Abstract
We will study bounded linear operators defined on real or complex Banach or Hilbert spaces, as well as operators on finite-dimensional vector spaces over general fields. Various families of linear operators with additional algebraic structure, e. g. families that are semigroups, groups, vector spaces, associative algebras or Lie algebras will be studied. Our central problem will be the existence of a common invariant subspace of the family. Another class of problems comes from the consideration of the sets of operators as algebraic subsets, i.e. varieties in affine or projective spaces. Our next aim is to translate the theory of Banach algebras into the context of Banach modules. We are going to study representations of Banach modules, some spectra of these modules, and structure topologies on them. Next research goal is to develop representation theory for ordered associative rings with involution. In the commutative case the represenentations are just homomorphism. A noncommutative analogue of rings of continous functions are Cx-algebras and a noncommutative analogue of homomorphisms are irreducible representations.The open problems are to find a good definition of the enveloping Cx-algebra of an ordered associative ring with involution, to characterize Cx-algebras within the class of ordered associative rings with involution, to generalize Kadison-Dubois and Jacobi''s Representation Theorem to ordered associative rings with involution. We will consider also the theory of preservers. We intend to classify (possibly noninjective or nonsurjective) additive mappings, which either preserve rank-one idempotents, or else annihilate them. Our goal are also elementary operators and operator inequalities. We intend to find some applications in the theory of double operator inegrals. Furthermore we will try to characterize self-adjoint invertible operators with simple operator inequality and generalize this result to unitarily invariant norms as well.
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