2024/01/06 by Augustine, Athul, Garayev, M., Shankar, P. · 2 citations
#47B32 #52A10 #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA)
paper · doi:10.48550/arxiv.2401.03176
The Berezin range of a bounded operator T acting on a reproducing kernel Hilbert space H is the set B(T) := \⟨ Tkx,kx ⟩H : x ∈ X\, where kx is the normalized reproducing kernel for H at x ∈ X. In general, the Berezin range of an operator is not convex. Primarily, we focus on characterizing the convexity of the Berezin range for a class of composition operators acting on the Fock space on ℂ and the Dirichlet space of the unit disc \mathbbD. We prove an analogue of the elliptic range theorem for the unitarily equivalent Berezin range of an operator on a two-dimensional reproducing kernel Hilbert space and characterize the convexity of the unitarily equivalent Berezin range for a bounded operator T on a reproducing kernel Hilbert space H.