Algebraične metode v teoriji operatorjev (Slovene)

In the research we will consider the following topics: ? linear operators on real and complex Banach and Hilbert spaces and on Banach lattices, ? special classes of linear operators: compact, quasinilpotent, those similar to normal operators, and contractions, ? families of linear operators with some additional algebraic structure such as semigroups, groups, vector spaces, and Lie algebras, ? problems of joint invariant subspaces of families of linear operators, ? structure of maximal families of linear operators with some additional properties, ? possible generalizations ob new results to finite dimensional vector spaces over arbitrary fields. These problems are motivated by some classical results from the beginning of the century proved by Engel, Levitzki, Motzkin, Taussky and others. The starting points for the current research are results obtained by H. Radjavi, the principal investigator and other members of the group. Significance of the research program for the science in general: Possible results are of importance in the development of operator theory. Previous results of the research group were noted in the research of other foreign pure mathematicians. We expect that new results will have similar influence. We will continue our cooperation with a number of foreign mathematicians. We plan to expand cooperation and help our younger researchers to find international contacts. Significance of the research program for Slovenia: The proposed research program will help in development of algebra and operator theory in Slovenia. We expect to further the respectability for Slovenian mathematical school. The program continues the research commenced by internationally recognized mathematicians Plemelj and Vidav. It is also important for the development of current and future generations of young researchers. Visiting foreign researchers provide a direct contact for younger researchers with the current development of mathematics.