Yuliya P. Moskaleva, Yurii S. Samoilenko, “On Transitive Systems of Subspaces in a Hilbert Space”, SIGMA, 2006, Volume 2,042, 19 pp.

On Transitive Systems of Subspaces in a Hilbert Space

Yuliya P. Moskaleva^a, Yurii S. Samoilenko^b

^a Taurida National University, 4 Vernads’kyi Str., Simferopol, 95007 Ukraine
^b Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivs'ka Str., Kyiv-4, 01601 Ukraine

Abstract: Methods of $*$-representations in Hilbert space are applied to study of systems of $n$ subspaces in a linear space. It is proved that the problem of description of $n$-transitive subspaces in a finite-dimensional linear space is $*$-wild for $n\geq 5$.

Keywords: algebras generated by projections; irreducible inequivalent representations; transitive nonisomorphic systems of subspaces.

MSC: 47A62; 16G20

Received: February 27, 2006; Published online April 12, 2006

Language: English

DOI: 10.3842/SIGMA.2006.042