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 :
| Szerző: | |
|---|---|
| Dokumentumtípus: | Cikk |
| Megjelent: |
2021
|
| 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 |
| Tartalmi kivonat: | 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. |
|---|---|
| Terjedelem/Fizikai jellemzők: | 265-294 |
| ISSN: | 2064-8316 |