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...

Teljes leírás

Elmentve itt :
Bibliográfiai részletek
Szerző: Arnold Loris
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
Leíró adatok
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