Some remarks on Hilbert representations of posets

2013/12/10 by Ostrovskyi, Vasyl, Rabanovich, Slavik
#15A24 (Primary) 16G20 #47A62 (Secondary) #FOS: Mathematics #Operator Algebras (math.OA) #Representation Theory (math.RT) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1312.2920

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.

Related

• Unitarization of linear representations of non-primitive posets
• Topological Representations of Posets
• Stable representations of posets
• Matrix Problems in Hilbert Spaces
• Operator residuation in orthomodular posets of finite height