5 research outputs found
Algebras of Toeplitz operators on the n-dimensional unit ball
We study -algebras generated by Toeplitz operators acting on the standard weighted Bergman space over the unit ball in . The symbols of generating operators are assumed to be of a certain product type, see (\ref{Introduction_form_of_the_symbol}). By choosing and in different function algebras and over lower dimensional unit balls and , respectively, and by assuming the invariance of under some torus action we obtain -algebras whose structural properties can be described. In the case of -quasi-radial functions and bounded uniformly continuous
or vanishing oscillation symbols we describe the structure of elements from the algebra , derive a list of irreducible
representations of , and prove completeness of this list in some cases. Some of these representations originate from a ``quantization effect'', induced
by the representation of as the direct sum of Bergman spaces over a lower dimensional unit ball with growing weight parameter. As an application we derive the
essential spectrum and index formulas for matrix-valued operators