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Wold-type extension for N-tuples of commuting contractions

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Kosiek M., Octavio A.

Studia Mathematica

1999

tom 137

nr 1

81-91

Let (T_1,…,T_N) 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 (V_1,…,V_N) of contractions on a superspace K of ℋ such that each $V_j$ extends $T_j$, j=1,…,N, and the N-tuple (V_1,…,V_N) 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])

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1 Studia Mathematica

1 Kosiek M.

1 Octavio A.

1 1999

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Wold-type extension for N-tuples of commuting contractions