Displaying similar documents to “On dilation and commuting liftings of n-tuples of commuting Hilbert space contractions”

Standard commuting dilations and liftings

Santanu Dey (2012)

Colloquium Mathematicae

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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.

Special symmetries of Banach spaces isomorphic to Hilbert spaces

Jarno Talponen (2010)

Studia Mathematica

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We characterize Hilbert spaces among Banach spaces in terms of transitivity with respect to nicely behaved subgroups of the isometry group. For example, the following result is typical: If X is a real Banach space isomorphic to a Hilbert space and convex-transitive with respect to the isometric finite-dimensional perturbations of the identity, then X is already isometric to a Hilbert space.

Perturbations of operators similar to contractions and the commutator equation

C. Badea (2002)

Studia Mathematica

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Let T and V be two Hilbert space contractions and let X be a linear bounded operator. It was proved by C. Foiaş and J. P. Williams that in certain cases the operator block matrix R(X;T,V) (equation (1.1) below) is similar to a contraction if and only if the commutator equation X = TZ-ZV has a bounded solution Z. We characterize here the similarity to contractions of some operator matrices R(X;T,V) in terms of growth conditions or of perturbations of R(0;T,V) = T ⊕ V.

Squaring a reverse AM-GM inequality

Minghua Lin (2013)

Studia Mathematica

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Let A, B be positive operators on a Hilbert space with 0 < m ≤ A, B ≤ M. Then for every unital positive linear map Φ, Φ²((A + B)/2) ≤ K²(h)Φ²(A ♯ B), and Φ²((A+B)/2) ≤ K²(h)(Φ(A) ♯ Φ(B))², where A ♯ B is the geometric mean and K(h) = (h+1)²/(4h) with h = M/m.

A class of generalized-Hilbert-Schmidt operators

B. E. Rhoades (1975)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

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G. H. Constantin ha definito una classe di operatori di Cesàro-Hilbert-Schmidt. In questa Nota l'Autore trova la corrispondente proprietà per una più generale classe di operatori di Hilbert-Schmidt (G. H. S.).