Functional Analysis and Applications Seminar 

29/10/2009, 15:00 — 16:00 — Room P3.10, Mathematics Building
Borut Zalar, University of Maribor, Slovenia

Computation of norms of several operators on matrix spaces arising from Jordan algebra

We will present some results and open problems concerning norms of some operators acting on a Hilbert space and even operator norms of matrices. The origin of this norm-computation problems is nonassociative algebra, which will also be briefly explained. We will consider some Jordan structures possesing models that can be represented as subspaces of the algebra of bounded operators on a Hilbert space. Even in this special cases norms of several algebraic operators (Jacobson-McCrimmon operator) are surprisingly difficult to compute, even in just two-dimensional case. This gives rise to several interesting problems, which can be understood without knowledge of nonassociative algebra and perhaps tackled by every student of functional analysis.