Sub-Bergman Hilbert spaces in the unit disk, II

Sub-Bergman Hilbert Spaces on the Unit Disk

If the contraction T is a Toeplitz operator on H2 or A2 induced by an analytic function φ, we then denote the resulting space by H(φ). Similarly, if T is the Toeplitz operator on H2 or A2 induced by a conjugate analytic symbol φ, then we denote the resulting space by H(φ). In the context of Hardy spaces, H(φ) and H(φ) are called sub-Hardy Hilbert spaces by Sarason in [6]. We thus arrive at the ...

Adjoints of Composition Operators on Standard Bergman and Dirichlet Spaces on the Unit Disk

It is not known a satisfactory way to compute adjoints of composition operators, yet in classical functional Banach spaces (cf. [3]). If K is the reproducing kernel of a functional Hilbert space H, g ∈ H and the composition operator Cφ is bounded then C∗ φg (z) = 〈g(t),K (z, φ (t))〉H , z ∈ D. In general, although reproducing kernels might be described in series developments, it is not possible ...

Compact Composition Operators on Bergman Spaces of the Unit Ball

Under a mild condition we show that a composition operator Cφ is compact on the Bergman space Aα of the open unit ball in C if and only if (1− |z|)/(1− |φ(z)|) → 0 as |z| → 1−.

Weighted composition operators between weighted Bergman spaces and Hardy spaces on the unit ball of C

In this paper, we study the weighted composition operators Wφ,ψ :f → ψ(f ◦ φ) between weighted Bergman spaces and Hardy spaces on the unit ball of Cn. We characterize the boundedness and the compactness of the weighted composition operators Wφ,ψ :Ap(να)→Aq(νβ) (0 < q < p <∞, −1 < α,β <∞) and Wφ,ψ :Hp(B)→Hq(B) (0 < q < p <∞). © 2006 Elsevier Inc. All rights reserved.

Generalized Frames in Hilbert Spaces