An index theorem for Toeplitz operators on the quarter-plane

Toeplitz Operators in a Quarter-plane by Gilbert Strang

An index theorem for Toeplitz operators on odd-dimensional manifolds with boundary

We establish an index theorem for Toeplitz operators on odd-dimensional spin manifolds with boundary. It may be thought of as an odd-dimensional analogue of the Atiyah–Patodi–Singer index theorem for Dirac operators on manifolds with boundary. In particular, there occurs naturally an invariant of η type associated to K1 representatives on even-dimensional manifolds, which should be of independe...

Representation and Index Theory for Toeplitz Operators

We study Toeplitz operators on the Hardy spaces of connected compact abelian groups and of tube-type bounded symmetric domains. A representation theorem for these operators and for classes of abstract Toeplitz elements in C*-algebras is proved. This is used to give a unified treatment to index theory in this setting, and a variety of new index theorems are proved that generalize the Gohberg–Kre...

Index Theory for Toeplitz Operators on Bounded Symmetric Domains

In this note we give an index theory for Toeplitz operators on the Hardy space of the Shilov boundary of an arbitrary bounded symmetric domain. Our results generalize earlier work of Gohberg-Krein and Venugopalkrishna [12] for domains of rank 1 and of Berger-Coburn-Koranyi [1] for domains of rank 2. Bounded symmetric domains (Cartan domains, classical or exceptional) are the natural higher-dime...

Criteria for Toeplitz Operators on the Sphere

Let H(S) be the Hardy space on the unit sphere S in C. We show that a set of inner functions Λ is sufficient for the purpose of determining which A ∈ B(H(S)) is a Toeplitz operator if and only if the multiplication operators {Mu : u ∈ Λ} on L(S, dσ) generate the von Neumann algebra {Mf : f ∈ L∞(S, dσ)}.