scholarly journals An index theorem for Toeplitz operators on totally ordered groups

1998 ◽  
Vol 126 (10) ◽  
pp. 2993-2998 ◽  
Author(s):  
Sriwulan Adji ◽  
Iain Raeburn ◽  
Anton Ströh
Keyword(s):  
Toeplitz Operators ◽  
Index Theorem ◽  
Ordered Groups

The Index Theory Associated to a Non-Finite Trace on a C*-Algebra

2005 ◽  
Vol 48 (2) ◽  
pp. 251-259 ◽  
Author(s):  
G. J. Murphy
Keyword(s):  
Compact Group ◽  
Representation Theorem ◽  
Toeplitz Operators ◽  
Von Neumann Algebra ◽  
Index Theory ◽  
Index Theorem ◽  
Fredholm Index ◽  
Von Neumann ◽  
C Algebra ◽  
Finite Trace

AbstractThe index theory considered in this paper, a generalisation of the classical Fredholm index theory, is obtained in terms of a non-finite trace on a unitalC*-algebra. We relate it to the index theory of M. Breuer, which is developed in a von Neumann algebra setting, by means of a representation theorem. We show how our new index theory can be used to obtain an index theorem for Toeplitz operators on the compact group U(2), where the classical index theory does not give any interesting result.

A NOTE ON TOEPLITZ OPERATORS

1996 ◽  
Vol 07 (04) ◽  
pp. 501-513 ◽  
Author(s):  
ERIK GUENTNER ◽  
NIGEL HIGSON
Keyword(s):  
Riemannian Manifolds ◽  
Toeplitz Operators ◽  
Boundary Value ◽  
Bergman Spaces ◽  
Index Theorem ◽  
Value Theory ◽  
Point Of View ◽  
Dirac Type ◽  
Complete Manifolds ◽  
Complete Riemannian Manifolds

We study Toeplitz operators on Bergman spaces using techniques from the analysis of Dirac-type operators on complete Riemannian manifolds, and prove an index theorem of Boutet de Monvel from this point of view. Our approach is similar to that of Baum and Douglas [2], but we replace boundary value theory for the Dolbeaut operator with much simpler estimates on complete manifolds.

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