Abstract
We consider the C*-algebra generated by Toeplitz operators acting on the Bergman space over the upper half-plane whose symbols depend on the imaginary part of the argument only. Such algebra is known to be commutative, and is isometrically isomorphic to an algebra of bounded complex-valued functions on the positive half-line. In the paper we prove that the latter algebra consists of all bounded functions f that are very slowly oscillating in the sense that the composition of f with the exponential function is uniformly continuous or, in other words.
Original language | English |
---|---|
Pages (from-to) | 149-166 |
Number of pages | 18 |
Journal | Integral Equations and Operator Theory |
Volume | 77 |
Issue number | 2 |
DOIs | |
State | Published - Oct 2013 |
Keywords
- Bergman space
- Laplace transform
- Toeplitz operators
- invariant under horizontal shifts
- very slowly oscillating functions