Arnold Loris: Derivative bounded functional calculus of power bounded operators on Banach spaces. In: Acta scientiarum mathematicarum, (87) 1-2. pp. 265-294. (2021)
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Abstract
In this article we study bounded operators T on a Banach space X which satisfy the discrete Gomilko–Shi-Feng condition Z 2π 0 |hR(re it, T) 2 x, x i|dt ≤ C (r 2 − 1) kxk kx k , r > 1, x ∈ X, x∗ ∈ X We show that it is equivalent to a certain derivative bounded functional calculus and also to a bounded functional calculus relative to Besov space. Also on Hilbert spaces the discrete Gomilko–Shi-Feng condition is equivalent to powerboundedness. Finally we discuss the last equivalence on general Banach spaces involving the concept of γ-boundedness.
| Item Type: | Article |
|---|---|
| Heading title: | Analysis |
| Journal or Publication Title: | Acta scientiarum mathematicarum |
| Date: | 2021 |
| Volume: | 87 |
| Number: | 1-2 |
| ISSN: | 2064-8316 |
| Page Range: | pp. 265-294 |
| Language: | English |
| Related URLs: | http://acta.bibl.u-szeged.hu/73791/ |
| DOI: | 10.14232/actasm-020-040-y |
| Uncontrolled Keywords: | Banach-tér, Matematika |
| Additional Information: | Bibliogr.: p. 293-294. ; összefoglalás angol nyelven |
| Date Deposited: | 2021. Nov. 16. 09:23 |
| Last Modified: | 2021. Nov. 16. 09:23 |
| URI: | http://acta.bibl.u-szeged.hu/id/eprint/73929 |
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