Projections in rotation algebras, revisited
given at Berkeley: Rieffel Seminar (19.10.10)
As an application of the link between noncommutative geometry and time-frequency analysis I present some recent results on projections in rotation algebras. Rank-one operators over projective modules over rotation algebras are shown to be Gabor frame operators and I discuss the so-called Walnut representation and Janssen representation of these rank-one operators. Rieffel's construction of projections in rotation algebras turns out to be equivalent to the construction of tight Gabor frames for the space of square-integrable functions, which provide discrete variants of coherent states representations. In this approach to Rieffel's projections a class of Banach spaces, Wiener amalgam spaces, turns out to be very useful in the construction of projections in rotation algebras.