Index Theory for Multivariable Toeplitz Operators

1996 ◽  
pp. 371-461 ◽  
Author(s):  
Harald Upmeier
Keyword(s):  
Toeplitz Operators ◽  
Index Theory

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.

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