Systems of $n$ subspaces and representations of $*$-algebras generated by projections

Details Systems of $n$ subspaces and representations of $*$-algebras generated by projections Systems of $n$ subspaces and representations of $*$-algebras generated by projections

2006-03-21

arxiv.org/abs/math/0603503v1

Mathematics

Operator Algebras

19 pp., 2 figs

Scientific paper

In this paper we study a relationship between systems of $n$ subspaces and
representations of $*$-algebras generated by projections. We prove that
irreducible nonequivalent $*$-representations of $*$-algebras $\mathcal
P_{4,com}$ generate all nonisomorphic transitive quadruples of subspaces of a
finite dimensional space.

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