Non--Vanishing functions and Toeplitz Operators on Tube--Type Domains

Details Non--Vanishing functions and Toeplitz Operators on Tube--Type Domains Non--Vanishing functions and Toeplitz Operators on Tube--Type Domains

2009-09-30

arxiv.org/abs/0910.0036v2

Mathematics

Operator Algebras

Scientific paper

We prove an index theorem for Toeplitz operators on irreducible tube--type domains and we extend our results to Toeplitz operators with matrix symbols. In order to prove our index theorem, we proved a result asserting that a non--vanishing function on the Shilov boundary of a tube--type bounded symmetric domain, not necessarily irreducible, is equal to a unimodular function defined as the product of powers of generic norms times an exponential function.

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