Index of $Γ$-equivariant Toeplitz operators

Details Index of $Γ$-equivariant Toeplitz operators Index of $Γ$-equivariant Toeplitz operators

1999-11-08

arxiv.org/abs/math/9911042v1

Mathematics

Operator Algebras

17 pages

Scientific paper

Let $\Gamma$ be a discrete icc subgroup of PSL(2,R) of infinite covolume. and let M denote the quotient of the unit disc by $\Gamma$. We prove that a Toeplitz operator with $\Gamma$-invariant symbol f in C(M) is Brauer Fredholm if its symbol is invertible on the boundary of M and its Brauer index is equal to the winding number of f at the boundary. We construct the associated extension of the algebra of functions continuous on the boundary of M by the Brauer ideal in the C*-algebra generated by such operators.

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