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 : f ↦ ψ(f ○ φ) 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 : x ↦ ψ(⋅)x from X to Hv∞(X), in contrast to the familiar scalar-valued setting X = ℂ.
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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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