C*-Algebra Generated by Angular Toeplitz Operators on the Weighted Bergman Spaces Over the Upper Half-Plane

Abstract

We consider the set of all Toeplitz operators acting on the weighted Bergman space over the upper half-plane whose L∞-symbols depend only on the argument of the polar coordinates. The main result states that the uniform closure of this set coincides with the C * -algebra generated by the above Toeplitz operators and is isometrically isomorphic to the C * -algebra of bounded functions that are very slowly oscillating on the real line in the sense that they are uniformly continuous with respect to the arcsinh-metric on the real line.Mathematics Subject Classification. Primary: 47B35; Secondary: 32A36.

Translation-invariant operators in reproducing kernel Hilbert spaces

“…The spectral functions of angular Toeplitz operators can be computed by This formula coincides with [37, Theorem 7.2.1], see also [13]. The C*-algebra G for this example is found by Esmeral, Maximenko, and Vasilevski [9]. Example 9.11 (the radial basis function kernel on the complex domain).…”

Radial Toeplitz Operators on the Fock Space and Square-Root-Slowly Oscillating Sequences

“…This result extends to weighted Bergman spaces over the unit ball [3,20]. Recent studies [11,17,19,25] have given explicit descriptions of commutative C*-algebras generated by vertical and angular Toeplitz operators on Bergman spaces. This paper focuses on studying the C*-algebra generated by radial Toeplitz operators acting on Fock spaces.…”

Toeplitz Operators Defined by Sesquilinear Forms: Bergman Space Case

“…Angular operators Recall [4], that the angular operators S (acting on A 2 (Π)) are those that commute with the group of dilation operators (…”

“…The C * -algebra generated by angular Toeplitz operators with bounded symbols is isomorphic [4] to the algebra VSO(R), which consists of those functions in L ∞ (R) that are uniformly continuous with respect to the arcsinh-metric ρ(x, y) = |arcsinh x − arcsinh y| .…”