Weighted composition operators from Bloch-type spaces into growth spaces on the unit ball of a Hilbert space

Abstract

Let ν, μ be normal weights on the unit ball BX of an Hilbert space X with arbitrary dimension and ψ be a holomorphic function on BX and φ a holomorphic self-map of BX. In this work, we characterize the boundedness and the compactness of weighted composition operators Wψ,φ, f 7→ ψ · (f ◦ φ), from the Bloch-type spaces Bν(BX) to the (little) growth spaces H∞ μ (BX), H0μ (BX) via function theoretic properties of the symbol ψ and the point evaluation function δBν(BX) φ(z) , specifically, of the restrictions of functions ψ, φ to the m-dimensional subspaces for some m ≥ 2. We also obtain the formula of the operator norm of Wψ,φ.