Isometric parts of operators and the critical exponent
Vlastimil Pták (1976)
Časopis pro pěstování matematiky
Similarity:
Vlastimil Pták (1976)
Časopis pro pěstování matematiky
Similarity:
Zbigniew Burdak, Wiesław Grygierzec (2020)
Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica
Similarity:
The n-tuples of commuting Hilbert space contractions are considered. We give a model of a commuting lifting of one contraction and investigate conditions under which a commuting lifting theorem holds for an n-tuple. A series of such liftings leads to an isometric dilation of the n-tuple. The method is tested on some class of triples motivated by Parrotts example. It provides also a new proof of the fact that a positive definite n-tuple has an isometric dilation.
Marek Kosiek, Alfredo Octavio (1999)
Studia Mathematica
Similarity:
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])
I. Halperin (1963)
Studia Mathematica
Similarity:
Vladimír Kordula (1993)
Czechoslovak Mathematical Journal
Similarity:
Bernard Morrel, Paul Muhly (1974)
Studia Mathematica
Similarity:
William F. Donoghue (1963)
Publications Mathématiques de l'IHÉS
Similarity:
Santanu Dey (2012)
Colloquium Mathematicae
Similarity:
We identify how the standard commuting dilation of the maximal commuting piece of any row contraction, especially on a finite-dimensional Hilbert space, is associated to the minimal isometric dilation of the row contraction. Using the concept of standard commuting dilation it is also shown that if liftings of row contractions are on finite-dimensional Hilbert spaces, then there are strong restrictions on properties of the liftings.