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Ranges of vector states on irreducible operator semigroups

Lookup NU author(s): Dr Alexey Popov

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Abstract

Let be a linear functional of rank one acting on an irreducible semigroup of operators on a finite- or infinite-dimensional Hilbert space. It is a well-known and simple fact that the range of 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 with a two-element range yields valuable information on the structure of .

Publication metadata

Author(s): Marcoux LW, Omladic M, Popov AI, Radjavi H, Yahaghi BR

Publication type: Article

Publication status: Published

Journal: Semigroup Forum

Year: 2016

Volume: 93

Issue: 2

Pages: 264-304

Print publication date: 01/10/2016

Online publication date: 07/01/2016

Acceptance date: 09/12/2015

ISSN (print): 0037-1912

ISSN (electronic): 1432-2137

Publisher: Springer

URL: http://dx.doi.org/10.1007/s00233-015-9772-7

DOI: 10.1007/s00233-015-9772-7

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