Displaying similar documents to “Decompositions of operator-valued functions in Hilbert spaces”

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])

Canonical functional extensions on von Neumann algebras

Carlo Cecchini (1999)

Studia Mathematica

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The topology and the structure of the set of the canonical extensions of positive, weakly continuous functionals from a von Neumann subalgebra M 0 to a von Neumann algebra M are described.