Derivative bounded functional calculus of power bounded operators on Banach spaces
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 bou...
Elmentve itt :
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| Dokumentumtípus: | Cikk |
| Megjelent: |
2021
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| Sorozat: | Acta scientiarum mathematicarum
87 No. 1-2 |
| Kulcsszavak: | Banach-tér, Matematika |
| doi: | 10.14232/actasm-020-040-y |
| Online Access: | http://acta.bibl.u-szeged.hu/73929 |
| LEADER | 01292nab a2200205 i 4500 | ||
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| 008 | 211116s2021 hu o 0|| eng d | ||
| 022 | |a 2064-8316 | ||
| 024 | 7 | |a 10.14232/actasm-020-040-y |2 doi | |
| 040 | |a SZTE Egyetemi Kiadványok Repozitórium |b hun | ||
| 041 | |a eng | ||
| 100 | 1 | |a Arnold Loris | |
| 245 | 1 | 0 | |a Derivative bounded functional calculus of power bounded operators on Banach spaces |h [elektronikus dokumentum] / |c Arnold Loris |
| 260 | |c 2021 | ||
| 300 | |a 265-294 | ||
| 490 | 0 | |a Acta scientiarum mathematicarum |v 87 No. 1-2 | |
| 520 | 3 | |a 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. | |
| 695 | |a Banach-tér, Matematika | ||
| 856 | 4 | 0 | |u http://acta.bibl.u-szeged.hu/73929/1/math_087_numb_001-002_265-294.pdf |z Dokumentum-elérés |