Multipliers of Hardy spaces, quadratic integrals and Foiaş-Williams-Peller operators

Blower, G.

Blower, G.

Studia Mathematica, Tome 129 (1998), p. 179-188 / Harvested from The Polish Digital Mathematics Library

Résumé

We obtain a sufficient condition on a B(H)-valued function φ for the operator $⨍ \mapsto Γ_{φ} ⨍^{'} (S)$ to be completely bounded on $H^{\infty} B (H)$ ; the Foiaş-Williams-Peller operator | St Γφ | Rφ = | | | 0 S | is then similar to a contraction. We show that if ⨍ : D → B(H) is a bounded analytic function for which $(1 - r) | | ⨍^{'} (r e^{i θ}) {| |}_{B (H)}^{2} r d r d θ$ and $(1 - r) | | ⨍ " (r e^{i θ}) {| |}_{B (H)} r d r d θ$ are Carleson measures, then ⨍ multiplies ${(H^{1} c^{1})}^{'}$ to itself. Such ⨍ form an algebra A, and when φ’∈ BMO(B(H)), the map $⨍ \mapsto Γ_{φ} ⨍^{'} (S)$ is bounded $A \to B (H^{2} (H), L^{2} (H) ⊖ H^{2} (H))$ . Thus we construct a functional calculus for operators of Foiaş-Williams-Peller type.

Publié le : 1998-01-01

Zbl 0926.47015

EUDML-ID : urn:eudml:doc:216574

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     author = {G. Blower},
     title = {Multipliers of Hardy spaces, quadratic integrals and Foia\c s-Williams-Peller operators},
     journal = {Studia Mathematica},
     volume = {129},
     year = {1998},
     pages = {179-188},
     zbl = {0926.47015},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv131i2p179bwm}
}

Blower, G. Multipliers of Hardy spaces, quadratic integrals and Foiaş-Williams-Peller operators. Studia Mathematica, Tome 129 (1998) pp. 179-188. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv131i2p179bwm/

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