On Fourier orthogonal projections in the rotation algebra

Details On Fourier orthogonal projections in the rotation algebra On Fourier orthogonal projections in the rotation algebra

2000-12-07

arxiv.org/abs/math/0012053v1

Mathematics

Operator Algebras

16 pages, preprint

Scientific paper

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, that 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.

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