Vertical symbols, Toeplitz operators on weighted Bergman spaces over the upper half-plane and very slowly oscillating functions

Abstract

Extending a recent result of Herrera Yañez, Maximenko and Vasilevski, we provide a further step in the structural analysis of algebras generated by Toeplitz operators on weighted Bergman spaces over the upper half-plane. We show that the set of “spectral” functions corresponding to Toeplitz operators generated by bounded vertical symbols is dense in the C⁎-algebra of very slowly oscillating functions on the positive half-line.