Abstract
We consider the C∗-algebra generated by Toeplitz operators acting on the Bergman space over the upper half-plane whose symbols depend only on the argument of the variable. This algebra is known to be commutative, and it is isometrically isomorphic to a certain algebra of bounded complex-valued functions on the real numbers. In the paper we prove that the latter algebra consists of all bounded functions f that are very slowly oscillating on the real line in the sense that the composition of f with sinh is uniformly continuous with respect to the usual metric.
Original language | English |
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Pages (from-to) | 151-162 |
Number of pages | 12 |
Journal | Communications in Mathematical Analysis |
Volume | 17 |
Issue number | 2 |
State | Published - 2014 |
Keywords
- Bergman space
- Invariant under dilatation
- Slowly oscillating function
- Toeplitz operator