Direct limits of operators in the Hilbert space

Abstract

We present an application of the direct (inductive) limit approach to Toeplitz operators on Segal–Bargmann space. The space corresponds to some analytic functions of infinitely many variables that are square integrable with respect to a Gaussian measure. There are different approaches to such operators that only seem equivalent but lead to different properties of Toeplitz operators. Among the used tools are tensor products, isometric inductive limits and frames.