Displaying similar documents to “On semi-groups of contractions in Hilbert spaces”

Unitary dilations of contraction operators

W. Mlak

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ContentsPreliminaries.................................................................................... 31. Notation and definitions............................................................. 62. Simple unitary dilations............................................................. 83. Dilation theorem.......................................................................... 124. Unitary dilation of a single contractions.................................. 225. Decomposition theorems............................................................

Wold-type extension for N-tuples of commuting contractions

Marek Kosiek, Alfredo Octavio (1999)

Studia Mathematica

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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])