Abstract. D. Westood (J. Funct. Anal. 66 (1986), 96-104) proved that Coocontractions with dominating spectrum are in A«0 . We generalize this result to polynomially bounded operators.
Abstract. In this paper we give a necessary and sufficient condition for the central intertwining lifting of a strict contraction to be strictly contractive. As an application, we obtain a factorization of D
−2Ac when the central intertwining lifting Ac of A is a strict contraction.Let H, H be (complex, separable) Hilbert spaces, T and T contractions in L(H) and L(H ), respectively, having minimal isometric dilations U and U in L(K) and L(K ). If A is a contraction operator in L(H, H ) such that AT = T A, the celebrated Sz.-Nagy-Foias commutant lifting theorem ([3, 7, 8] | kerT * is invertible (see [5]). For the convenience of the reader we begin by reviewing some notation and terminology (see [3,4,5,6,8] . Since the minimal isometric dilation of T is unique (up to an isomorphism (see [3,8])), we may and do assume that U ∈ L(K ), the minimal isometric dilation of T is the Sz.-Nagy-Schäffer minimal isometric dilation of T , i.e. K = H ⊕H 2 (D T ) and U
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