An index theorem for multivariable Toeplitz operators
The structure theory of the Toeplitz \(C^*\)-algebra \({\mathcal T}\) over a bounded symmetric domain D of rank r [cf. \textit{H. Upmeier}, Ann. Math., II. Ser. 119, 549-576 (1984; Zbl 0549.46031)] implies that there exist r analytical Fredholm indices for operators in \({\mathcal T}\), which are in general K-theory valued and ''live'' on the strata of the boundary of D. In this paper a topological formula for the ''highest'' r-index is given, using the Bott element of certain sphere bundles defined in Jordan algebraic terms. More recently, the author found topological index formula for al j-indices (1\(\leq j\leq r)\), in particular for the usual integer-valued (1-) index.
sphere bundles defined in Jordan algebraic terms
scientific article; zbMATH DE number 3946966
scientific article