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ON FOURIER ORTHOGONAL PROJECTIONS IN THE ROTATION ALGEBRA

Published online by Cambridge University Press:  08 August 2003

S. WALTERS
S. WALTERS
Affiliation:
Department of Mathematics and Computer Science, University of Northern British Columbia, Prince George, BC V2N 4Z9, Canadawalters@hilbert.unbc.ca, walters@unbc.ca
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Abstract

Projections are constructed in the rotation algebra that are orthogonal to their Fourier transform and which are fixed under the flip automorphism. Such projections are expected in a construction of an inductive limit structure for the irrational rotation algebra that is invariant under the Fourier transform (namely, as two circle algebras of the same dimension, which are swapped by the Fourier transform, plus a few points). The calculation is based on Rieffel's construction of the Schwartz space as an equivalence bimodule of rotation algebras as well as on the theory of theta functions.

Keywords

46L8046L40
Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 68 , Issue 1 , August 2003 , pp. 193 - 205
Copyright
The London Mathematical Society 2003

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Footnotes

Research partly supported by NSERC grant OGP0169928.