- June 22, 2009 , Monday - 16h00 (Room P
3.10):
On n-subspaces of Hilbert space
Roman Grushevoy
(Institute of Mathematics, National Academy of Science,
Kiev, Ukraine)
Abstract. 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 Hi one can
connect an orthoprojector Pi 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.
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