COMPLETELY CONTRACTIVE REPRESENTATIONS FOR SOME DOUBLY GENERATED ANTISYMMETRIC OPERATOR-ALGEBRAS

Contractive weak star continuous representations of the Fourier binest algebra A (of Katavolos and Power) are shown to be completely contrac tive. The proof depends on the approximation of A by semicrossed produ ct algebras A(IID) x Z(+) and on the complete contractivity of contrac tive representations of such algebras. The latter result is obtained b y two applications of the Sz.-Nagy-Foias lifting theorem. In the prese nce of an approximate identity of compact operators it is shown that a n automorphism of a general weakly closed operator algebra is necessar ily continuous for the weak star topology and leaves invariant the sub algebra of compact operators. This fact and the main result are used t o show that isometric automorphisms of the Fourier binest algebra are unitarily implemented.