W ∗ k = {x ǫX|xǫ Domain (A(a1) . . .A (ak)) for all a1, . . . , akǫA} is dense inX in theweak* topology. Let {e1, . . . , en} be a basis forA and setAi = A(ei), A ∗ i = A(ei). If α = (α1, . . . , αk), 1 ≤ αi ≤ n, is a sequence of integers we denote a product such as Aα1 . . .Aαk byAα; |α| = k is the length ofα. The operatorB ◦ = Σ|α|≤maαAα (the coefficients are complex numbers) is defined on Wm...

The algebra Ψ(M) of order zero pseudodifferential operators on a compact manifold M defines a well-known C∗-extension of the algebra C(S∗M) of continuous functions on the cospherical bundle S∗M ⊂ T ∗M by the algebra K of compact operators. In his proof of the index theorem, Higson defined and used an asymptotic homomorphism T from C0(T ∗M) to K, which plays the role of a deformation for the com...