2025/02/25 by Michael Hartz, Hartz, Michael, Maximilian Tornes +1
Mathematics · #47B33 #Advanced Banach Space Theory #Advanced Topics in Algebra #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Primary 46E22 #Secondary 47B32
paper · pdf · doi:10.48550/arxiv.2502.18301
openalex publication_date 2025/02/25 · openalex created_date 2025/10/15 · openalex updated_date 2026/07/28
A weighted composition operator on a reproducing kernel Hilbert space is given by a composition, followed by a multiplication. We study unitary and co-isometric weighted composition operators on unitarily invariant spaces on the Euclidean unit ball \mathbb Bd. We establish a dichotomy between the spaces Hγ with reproducing kernel (1 - ⟨ z,w ⟩)-γ for γ> 0, and all other spaces. Whereas the former admit many unitary weighted composition operators, the latter only admit trivial ones. This extends results of Martín, Mas and Vukotić from the disc to the ball. Some of our results continue to hold when d = ∞.