Bounded below composition operators on the space of Bloch functions on the unit ball of a Hilbert space

Let B-E be the open unit ball of a complex finite or infinite dimensional Hilbert space E and consider the space B(B-E) of Bloch functions on B-E. Using Lipschitz continuity of the dilation map on B-E given by x -> (1 - parallel to x parallel to(2))Rf(x) for x is an element of B-E, where Rf denotes the radial derivative of f is an element of B(B-E), we study when a composition operator on B(B-E) is bounded below.

Automated summary

This article studies the boundedness of composition operators on B(B-E), which are defined on the open unit ball B-E and involve Bloch functions.