2016/10/06 by Katsunori Kawamura, Kawamura, Katsunori
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Holomorphic and Operator Theory
paper · pdf · doi:10.48550/arxiv.1610.01818
For an arbitrary state ω on a Cuntz algebra, we define a number 1≤ κ(ω)≤ ∞ such that if the GNS representations of ω and ω' are unitarily equivalent, then κ(ω)=κ(ω'). By using κ, we define minimal states and it is shown that the classification problem of states is reduced to that of minimal states. By using results of Dutkay, Haussermann, and Jorgensen, we give a sufficient condition of the minimality of a state. Properties of κ and examples are shown. As an application, a new invariant of a certain class of endomorphisms of \cal B(\cal H) is given.