Toeplitz projections and essential commutants

We construct a Toeplitz projection for every regular A-Isometry T is an element of B(H)(n) on a complex Hilbert space H and use it to determine the essential commutant of the set of all analytic Toeplitz operators formed with respect to an essentially normal regular A-isometry. We show that the Toeplitz projection annihilates the compact operators if and only if T possesses no joint eigenvalues. As an application we deduce an essential version of the classical Hartman-Wintner spectral inclusion theorem, give a new proof of Johnson and Parrot's theorem on the essential commutant of abelian von Neumann algebras for separable Hilbert spaces and construct short exact sequences of Toeplitz algebras. (C) 2015 Elsevier Inc. All rights reserved.