Abstract
We show that, given a reflexive Banach space and a generator of an exponentially stable $C_{0}$-semigroup, a weakly admissible operator $g(A)$ can be defined for any $g$ bounded, analytic function on the left half-plane. This yields an (unbounded) functional calculus. The construction uses a Toeplitz operator and is motivated by system theory. In separable Hilbert spaces, we even get admissibility. Furthermore, it is investigated when a bounded calculus can be guaranteed. For this we introduce the new notion of exact observability by direction.
Original language | English |
---|---|
Pages (from-to) | 796-815 |
Number of pages | 20 |
Journal | Indagationes mathematicae |
Volume | 23 |
Issue number | 4 |
DOIs | |
Publication status | Published - Dec 2012 |
Keywords
- MSC-47A60
- MSC-47B35
- MSC-47D06
- MSC-93C25
- Weak admissibility
- Operator semigroup
- Functional calculus
- H-infinity
- Toeplitz operator
- Exact observability by direction