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On Fourier orthogonal projections in the rotation algebra

2000/12/07 by Sam Walters, Walters, Sam
Mathematics · #46L40 #46L80 #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA) #math.FA #math.OA #msc:46L40 #msc:46L80

paper · pdf · doi:10.48550/arxiv.math/0012053

16 pages, preprint

arxiv created 2000/12/07 · arxiv updated 2009/11/30

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, 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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