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1

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

100%

Blower G.

Studia Mathematica

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1998

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tom 131

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nr 2

179-188

EN

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.

2

Abel means of operator-valued processes

100%

Blower G.

Studia Mathematica

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1995

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tom 115

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nr 3

261-276

EN

Let $(X_j)$ be a sequence of independent identically distributed random operators on a Banach space. We obtain necessary and sufficient conditions for the Abel means of $X_n...X_2 X_1$ to belong to Hardy and Lipschitz spaces a.s. We also obtain necessary and sufficient conditions on the Fourier coefficients of random Taylor series with bounded martingale coefficients to belong to Lipschitz and Bergman spaces.

3

A multiplier characterization of analytic UMD spaces

26%

Blower G.

Studia Mathematica

|

1990

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tom 96

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nr 2

117-124

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3 Studia Mathematica

3 Blower G.

1 1998

1 1995

1 1990

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

Abel means of operator-valued processes

A multiplier characterization of analytic UMD spaces