Ranges of vector states on irreducible operator semigroups
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Date
2016
Authors
Marcoux, L.W.
Omladič, M.
Popov, A.I.
Radjavi, H.
Yahaghi, B.
Journal Title
Journal ISSN
Volume Title
Publisher
Springer
Abstract
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.
Description
This is a post-peer-review, pre-copyedit version of an article published in Semigroup Forum. The final authenticated version is available online at: https://doi.org/10.1007/s00233-015-9772-7
Keywords
irreducible operator semigroups, ranges of vector states, semigroups of small rank, compact groups of unitary matrices, selfadjoint semigroups