Ranges of vector states on irreducible operator semigroups
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Let 𝜑 be a linear functional of rank one acting on an irreducible semigroup S of operators on a finite- or infinite-dimensional Hilbert space. It is a well-known and simple fact that the range of 𝜑 cannot be a singleton. We start a study of possible finite ranges for such functionals. In particular, we prove that in certain cases, the existence of a single such functional 𝜑 with a two-element range yields valuable information on the structure of S.
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L.W. Marcoux, M. Omladič, A.I. Popov, H. Radjavi, B. Yahaghi (2016). Ranges of vector states on irreducible operator semigroups. UWSpace. http://hdl.handle.net/10012/15730