Abstract
LetF andG be elements of aC *-algebraA. Assume that, for each irreducible*-representationπ ofA on a Hilbert space210B; π , there is a bounded linear operatorL π ∈B(ℋ π ) such that the spectrum ofπ(F) −π(G)L π is contained in the open left half plane. We prove that there is then an elementL ∈A such that the spectrum ofF — GL is contained in the open left half plane. That is, if the system (F, G) is locally stabilizable, then it is stabilizable. We also consider the analogous problem with the open left half plane replaced by the open unit disk.
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This paper was supported in part by the National Science Foundation under Grant NSF-MCS-8002138.
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Bunce, J.W. Stabilizability of linear systems defined overC *-algebras. Math. Systems Theory 18, 237–250 (1985). https://doi.org/10.1007/BF01699471
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DOI: https://doi.org/10.1007/BF01699471