Bounded point evaluation for a finitely multicyclic commuting tuple of operators (Q785431)

The author introduces and establishes the basic properties of bounded point evaluations for a finitely multicyclic commuting \(d\)-tuple \(T=(T_1,\dots, T_d)\) of bounded linear operators on a complex separable Hilbert space \(H\). He shows that the set \(bpe(T)\) of all bounded point evaluations for \(T\) is a unitary invariant and characterizes it in terms of the dimension of the joint cokernel of \(T\). Furthermore, he characterizes the set of all analytic bounded point evaluations for \(T\), which is the largest open subset of \(bpe(T)\) on which all the elements of \(H\) are analytic. As an application, he describes the set of all analytic bounded point evaluations for toral and spherical isometries, and also derives an analytic model of a commuting \(d\)-tuple of composition operators.