### Abstract

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 |

### Fingerprint

### Keywords

- MSC-47A60
- MSC-47B35
- MSC-47D06
- MSC-93C25
- IR-82456
- Weak admissibility
- Operator semigroup
- EWI-22631
- METIS-296163
- Functional calculus

### Cite this

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*Indagationes mathematicae*, vol. 23, no. 4, pp. 796-815. https://doi.org/10.1016/j.indag.2012.04.005

**Weakly admissible H-calculus on reflexive Banach spaces.** / Schwenninger, F.L.; Zwart, Heiko J.

Research output: Contribution to journal › Article › Academic › peer-review

TY - JOUR

T1 - Weakly admissible H-calculus on reflexive Banach spaces

AU - Schwenninger, F.L.

AU - Zwart, Heiko J.

PY - 2012/12

Y1 - 2012/12

N2 - 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.

AB - 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.

KW - MSC-47A60

KW - MSC-47B35

KW - MSC-47D06

KW - MSC-93C25

KW - IR-82456

KW - Weak admissibility

KW - Operator semigroup

KW - EWI-22631

KW - METIS-296163

KW - Functional calculus

U2 - 10.1016/j.indag.2012.04.005

DO - 10.1016/j.indag.2012.04.005

M3 - Article

VL - 23

SP - 796

EP - 815

JO - Indagationes mathematicae

JF - Indagationes mathematicae

SN - 0019-3577

IS - 4

ER -