Anzeige
Erschienen in:
2008 | OriginalPaper | Buchkapitel
Commuting Toeplitz Operators and Hyperbolic Geometry
Erschienen in: Commutative Algebras of Toeplitz Operators on the Bergman Space
Verlag: Birkhäuser Basel
Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.
Wählen Sie Textabschnitte aus um mit Künstlicher Intelligenz passenden Patente zu finden. powered by
Markieren Sie Textabschnitte, um KI-gestützt weitere passende Inhalte zu finden. powered by
The
C
*
-algebras of Toeplitz operators considered in Chapters 5, 6, and 7 are commutative. This property is impossible (except for the trivial case of scalar operators ≡ constant defining symbols) for the
C
*
-algebras of Toeplitz operators acting on the Hardy space. The special features of the defining symbols which make this phenomenon possible were
symbols depending only on the imaginary part of a variable
for Toeplitz operators on the upper half-plane,
radial symbols
for Toeplitz operators on the unit disk, and
symbols depending only on the angular part of a variable
for Toeplitz operators on the upper half-plane, respectively. In this stage a natural question appears:
whether there exist other classes of defining symbols which generate commutative Toeplitz operator C
*
-
algebras, and how they can be classfied
.