Resumen de Projective multi-resolution analyses arising from direct limits of Hilbert modules

Nadia S. Larsen, Iain Raeburn

• The authors have recently shown how direct limits of Hilbert spaces can be used to construct multi-resolution analyses and wavelets in L2(R). Here they investigate similar constructions in the context of Hilbert modules over C*-algebras. For modules over C(Tn), the results shed light on work of Packer and Rieffel on projective multi-resolution analyses for specific Hilbert C(Tn)- modules of functions on Rn. There are also new applications to modules over C(C) when C is the infinite path space of a directed graph.