Some remarks on Hilbert representations of posets

Abstract

For a certain class of finite posets, we prove that all their irreducible orthoscalar representations are finite-dimensional and describe those, for which there exist essential (non-degenerate) irreducible orthoscalar representations.

15 pages

References in corpus (4)

• Locally-scalar representations of graphs in the category of Hilbert spaces
• Systems of subspaces of a unitary space
• On *-representations of a certain class of algebras related to a graph
• Unitarizable representations of quivers