Toeplitz Matrices acting on the ${\ell }^2$-space of an imprimitivity bimodule

Abstract

We give a definition of Toeplitz matrix acting on the ${\ell }^2$-space of an imprimitivity bimodule $X$ over a $C^{\ast }$-algebra $A$. We characterize the set of Toeplitz matrices as the closure in a certain topology of the image of the left regular representation of the crossed product $A⋊X$.

Background material has been added to the originally posted article