Convexity of the Berezin Range

Abstract

This paper discusses the convexity of the range of the Berezin transform. For a bounded operator $T$ acting on a reproducing kernel Hilbert space $H$ (on a set $X$), this is the set $B(T):=\{<T{k}_x,k_x{>}_H:x\in X\}$, where $k_x$ is the normalized reproducing kernel for $H$ at $x\in X$. Primarily, we focus on characterizing convexity of this range for a class of composition operators acting on the Hardy space of the unit disk.

Cited by in corpus (1)

• Berezin number and Berezin norm inequalities for operator matrices