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Admissible and weakly admissible observation operators for the right shift semigroup. (English) Zbl 1176.47065
Starting from the fact that weak admissibility implies infinite-time admissibility for \(T(t)\) in the case that \(T(t)\) is a semigroup of contractions right invertible and exponentially stable, G. Weiss conjectured that weak admissibility implies admissibility for the general case. In the meantime, a counterexample was found, showing that weak admissibility does not imply admissibility for analytic semigroups. In this paper, another example is presented showing that weak admissibility does not imply admissibility in the general case.

MSC:
47N70 Applications of operator theory in systems, signals, circuits, and control theory
47D06 One-parameter semigroups and linear evolution equations
93B28 Operator-theoretic methods
93B07 Observability
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