Unitary dilation and fixed point theorem
Marek Ptak (1989)
Annales Polonici Mathematici
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Marek Ptak (1989)
Annales Polonici Mathematici
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Najar, Rudolph M. (1995)
International Journal of Mathematics and Mathematical Sciences
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I. Suciu (1968)
Studia Mathematica
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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 extends , j=1,…,N, and the N-tuple (V1,…,VN) has a decomposition similar to the Wold-von Neumann decomposition for coisometries (although the need not be coisometries). As an application, we obtain a new proof of a result of Słociński (see [9])
Ching-I Hsin (2002)
Colloquium Mathematicae
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Let A be a complex n × n matrix. Let A' be its commutant in Mₙ(ℂ), and C(A) be its centralizer in GL(n,ℂ). Consider the standard C(A)-action on ℂⁿ. We describe the C(A)-orbits via invariant subspaces of A'. For example, we count the number of C(A)-orbits as well as that of invariant subspaces of A'.
Paul Muhly (1974)
Studia Mathematica
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G. Van Dijk, M. Poel (1986)
Compositio Mathematica
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I. Halperin (1963)
Studia Mathematica
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F. D. Veldkamp (1968)
Compositio Mathematica
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Wang, Ju-Kwei (1971)
Portugaliae mathematica
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Deitmar, Anton (2006)
International Journal of Mathematics and Mathematical Sciences
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Chafiq Benhida (2004)
Studia Mathematica
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Given two contractions T and T' such that T'-T is an operator of finite rank, we prove, under some conditions, the unitary equivalence of the unitary parts of the minimal isometric dilations (respectively minimal co-isometric extensions) of T and T'.
Aleksander Całka (1984)
Colloquium Mathematicae
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