$C*$-algebras generated by groups of composition operators

• Autores: Michael Jury
• Localización: Indiana university mathematics journal, ISSN 0022-2518, Vol. 56, Nº 6, 2007, págs. 3171-3192
• Idioma: inglés
• DOI: 10.1512/iumj.2007.56.3164
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• Resumen

  • We compute the C-algebra generated by a group of composition operators acting on certain reproducing kernel Hilbert spaces over the disk, where the symbols belong to a non-elementary Fuchsian group. We show that such a C-algebra contains the compact operators, and its quotient is isomorphic to the crossed product C-algebra determined by the action of the group on the boundary circle. In addition we show that the C-algebras obtained from composition operators acting on a natural family of Hilbert spaces are in fact isomorphic, and also determine the same Ext-class, which can be related to known extensions of the crossed product.