Functional Analysis and Applications Seminar 

22/06/2009, 16:00 — 17:00 — Room P3.10, Mathematics Building
Roman Grushevoy, Institute of Mathematics, National Academy of Science, Kiev, Ukraine

On $n$-subspaces of Hilbert space

The description of the system of $n$-subspaces of a linear space $V$ has become a classical problem of linear algebra. In particular, many works are devoted to the study of indecomposable fours of subspaces up to equivalence, representations of posets and other. We consider irreducible systems of n-subspaces of a Hilbert space $H$ up to unitary equivalence. With every subspace $H_i$ one can connect an orthoprojector $P_i$ on it and study irreducible $n$-tuples of orthoprojectors up to unitary equivalence. There is a well known list of all irreducible pairs of orthoprojectors (Halmos, 1965). But the description of irreducible three-tuples of orthoprojectors becomes a *-wild problem. So we add some conditions on subspaces of $H$ to describe them.