Abstract

We construct a nuclear, spectral invariant, dense Fréchet subalgebra C^∞(K) of the commutative algebra C(K) of continuous complex valued functions on the Cantor set K. The construction uses the group structure of the 2-adic integers on K.

We then use a smooth crossed product construction to get a dense, nuclear Fréchet subalgebra O₂ of the Cuntz algebra O₂. We prove the general result that a tempered action of a locally compact group on a strongly spectral invariant dense Fréchet subalgebra of a Banach algebra is automatically m-tempered, and obtain the m-convexity of O₂ as a special case.

Authors