Hyperinvariant subspace lattice of weak contractions

Michal Zajac

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Wold-type extension for N-tuples of commuting contractions

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Let (T1,…,TN) be an N-tuple of commuting contractions on a separable, complex, infinite-dimensional Hilbert space ℋ. We obtain the existence of a commuting N-tuple (V1,…,VN) of contractions on a superspace K of ℋ such that each $V_{j}$ extends $T_{j}$ , j=1,…,N, and the N-tuple (V1,…,VN) has a decomposition similar to the Wold-von Neumann decomposition for coisometries (although the $V_{j}$ need not be coisometries). As an application, we obtain a new proof of a result of Słociński (see [9])