### Operator-weighted composition operators on vector-valued analytic function spaces

Jussi Laitila and Hans-Olav Tylli
Source: Illinois J. Math. Volume 53, Number 4 (2009), 1019-1032.

#### Abstract

We study qualitative properties of the operator- weighted composition maps Wψ,φ : fψ(fφ) on the vector-valued spaces Hv(X) of X-valued analytic functions , where is the unit disk, X is a complex Banach space, φ is an analytic self-map of , ψ is an analytic operator-valued function on , and v is a bounded continuous weight on . Boundedness and compactness properties of Wψ,φ are characterized on Hv(X) for infinite-dimensional X. It turns out that the (weak) compactness of Wψ,φ also involves properties of the auxiliary operator Tψ : xψ(⋅)x from X to Hv(X), in contrast to the familiar scalar-valued setting X = ℂ.

First Page:
Primary Subjects: 47B33
Secondary Subjects: 46E40
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Permanent link to this document: http://projecteuclid.org/euclid.ijm/1290435336
Zentralblatt MATH identifier: 05824931
Mathematical Reviews number (MathSciNet): MR2741175

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