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

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

2007-01-10

arxiv.org/abs/math/0701276v1

Mathematics

Operator Algebras

Scientific paper

The authors have recently shown how direct limits of Hilbert spaces can be used to construct multi-resolution analyses and wavelets in $L^2(\R)$. Here they investigate similar constructions in the context of Hilbert modules over $C^*$-algebras. For modules over $C(\T^n)$, the results shed light on work of Packer and Rieffel on projective multi-resolution analyses for specific Hilbert $C(\T^n)$-modules of functions on $\R^n$. There are also new applications to modules over $C(C)$ when $C$ is the infinite path space of a directed graph.

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