K-theory of Toeplitz \(C^*\)-algebras on Lie spheres
Let D be a symmetric domain in the complex plane with the Shilov boundary \(S_ D\) and let \(P: L^ 2(S_ D)\to H^ 2(S_ D)\) be the orthogonal projection onto the Hardy space. The author considers the Toeplitz operators \(T_ f\phi =P(f\phi),\phi \in H^ 2(S_ D)\), with matricial symbols f. He computes the K-groups of the \(C^*\)-algebra of these operators and obtains the theorem on Fredholmness and index of \(T_ f\). This theorem generalises the similar result for scalar-valued symbol, see \textit{C. A. Berger}, \textit{L. A. Coburn} and \textit{A. Coranyi}, C. R. Acad. Sci., Paris, Sér. A 290, 989-991 (1980; Zbl 0436.47021).
orthogonal projection onto the Hardy space
scientific article; zbMATH DE number 4208850
scientific article