Details

Autor(en) / Beteiligte

• Bauer, Wolfram
• Hagger, Raffael
• Vasilevski, Nikolai

Titel

Algebras of Toeplitz Operators on the n-Dimensional Unit Ball

Ist Teil von

• Complex analysis and operator theory, 2019-03, Vol.13 (2), p.493-524

Ort / Verlag

Cham: Springer International Publishing

Erscheinungsjahr

2019

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• We study C ∗ -algebras generated by Toeplitz operators acting on the standard weighted Bergman space A λ 2 ( B n ) over the unit ball B n in C n . The symbols f ac of generating operators are assumed to be of a certain product type, see ( 1.1 ). By choosing a and c in different function algebras S a and S c over lower dimensional unit balls B ℓ and B n - ℓ , respectively, and by assuming the invariance of a ∈ S a under some torus action we obtain C ∗ -algebras T λ ( S a , S c ) of whose structural properties can be described. In the case of k -quasi-radial functions S a and bounded uniformly continuous or vanishing oscillation symbols S c we describe the structure of elements from the algebra T λ ( S a , S c ) , derive a list of irreducible representations of T λ ( S a , S c ) , and prove completeness of this list in some cases. Some of these representations originate from a “quantization effect”, induced by the representation of A λ 2 ( B n ) 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.