- Tytuł:
- Multipliers of Hardy spaces, quadratic integrals and Foiaş-Williams-Peller operators
- Autorzy:
- Blower, G.
- Powiązania:
- https://bibliotekanauki.pl/articles/1217911.pdf
- Data publikacji:
- 1998
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Tematy:
-
polynomially bounded operators
Hankel operators
multipliers
Carleson measures - Opis:
- We obtain a sufficient condition on a B(H)-valued function φ for the operator $⨍ ↦ Γ_φ ⨍'(S)$ to be completely bounded on $H^∞ B(H)$; the Foiaş-Williams-Peller operator | S^t Γ_φ | R_φ = | | | 0 S | is then similar to a contraction. We show that if ⨍ : D → B(H) is a bounded analytic function for which $(1-r) ||⨍'(re^{iθ})||^2_{B(H)} rdrdθ$ and $(1-r) ||⨍"(re^{iθ})||_{B(H)} rdrdθ$ are Carleson measures, then ⨍ multiplies $(H^1c^1)'$ to itself. Such ⨍ form an algebra A, and when φ'∈ BMO(B(H)), the map $⨍ ↦ Γ_φ ⨍'(S)$ is bounded $A → B(H^2(H), L^2(H) ⊖ H^2(H))$. Thus we construct a functional calculus for operators of Foiaş-Williams-Peller type.
- Źródło:
-
Studia Mathematica; 1998, 131, 2; 179-188
0039-3223 - Pojawia się w:
- Studia Mathematica
- Dostawca treści:
- Biblioteka Nauki
Artykuł