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

Studia Mathematica (1998)

- Volume: 131, Issue: 2, page 179-188
- ISSN: 0039-3223

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topBlower, G.. "Multipliers of Hardy spaces, quadratic integrals and Foiaş-Williams-Peller operators." Studia Mathematica 131.2 (1998): 179-188. <http://eudml.org/doc/216574>.

@article{Blower1998,

abstract = {We obtain a sufficient condition on a B(H)-valued function φ for the operator $⨍ ↦ Γ_φ ⨍^\{\prime \}(S)$ to be completely bounded on $H^∞ B(H)$; 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 $(1-r) ||⨍^\{\prime \}(re^\{iθ\})||^2_\{B(H)\} rdrdθ$ and $(1-r) ||⨍"(re^\{iθ\})||_\{B(H)\} rdrdθ$ are Carleson measures, then ⨍ multiplies $(H^1c^1)^\{\prime \}$ to itself. Such ⨍ form an algebra A, and when φ’∈ BMO(B(H)), the map $⨍ ↦ Γ_φ ⨍^\{\prime \}(S)$ 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.},

author = {Blower, G.},

journal = {Studia Mathematica},

keywords = {polynomially bounded operators; Hankel operators; multipliers; Carleson measures; completely bounded; Foiaş-Williams-Peller operator; functional calculus},

language = {eng},

number = {2},

pages = {179-188},

title = {Multipliers of Hardy spaces, quadratic integrals and Foiaş-Williams-Peller operators},

url = {http://eudml.org/doc/216574},

volume = {131},

year = {1998},

}

TY - JOUR

AU - Blower, G.

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

JO - Studia Mathematica

PY - 1998

VL - 131

IS - 2

SP - 179

EP - 188

AB - We obtain a sufficient condition on a B(H)-valued function φ for the operator $⨍ ↦ Γ_φ ⨍^{\prime }(S)$ to be completely bounded on $H^∞ B(H)$; 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 $(1-r) ||⨍^{\prime }(re^{iθ})||^2_{B(H)} rdrdθ$ and $(1-r) ||⨍"(re^{iθ})||_{B(H)} rdrdθ$ are Carleson measures, then ⨍ multiplies $(H^1c^1)^{\prime }$ to itself. Such ⨍ form an algebra A, and when φ’∈ BMO(B(H)), the map $⨍ ↦ Γ_φ ⨍^{\prime }(S)$ 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.

LA - eng

KW - polynomially bounded operators; Hankel operators; multipliers; Carleson measures; completely bounded; Foiaş-Williams-Peller operator; functional calculus

UR - http://eudml.org/doc/216574

ER -

## References

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