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

Abstract

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

19 pp., 2 figs

References in corpus (1)

• Relative position of four subspaces in a Hilbert space

Cited by in corpus (1)

• $n$-Subspaces in linear and unitary spaces