Displaying similar documents to “A note on general dilation theorems”

Extensions of the representation theorems of Riesz and Fréchet

João C. Prandini (1993)

Mathematica Bohemica

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We present two types of representation theorems: one for linear continuous operators on space of Banach valued regulated functions of several real variables and the other for bilinear continuous operators on cartesian products of spaces of regulated functions of a real variable taking values on Banach spaces. We use generalizations of the notions of functions of bounded variation in the sense of Vitali and Fréchet and the Riemann-Stieltjes-Dushnik or interior integral. A few applications...

On spectral representation for selfadjoint operators. Expansion in generalized eigenelements

Eberhard Gerlach (1965)

Annales de l'institut Fourier

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L’auteur reprend l’étude classique de la représentation spectrale d’un opérateur auto-adjoint A dans un espace de Hilbert ℋ . Il y ajoute des précisions nouvelles qui conduisent à la définition du projecteur infinitésimal P ) λ ) sur l’espace des vecteurs propres généralisés ℋ ( λ ) . Il obtient, par conséquent, des énoncés plus précis de bien des théorèmes classiques. Il introduit ensuite la notion de “ A -expansibilité” d’un sous-ensemble S ⊂ ℋ . Cette notion est appliquée à l’étude des espaces fonctionnels...

On an estimate for the norm of a function of a quasihermitian operator

M. Gil (1992)

Studia Mathematica

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Let A be a closed linear operator acting in a separable Hilbert space. Denote by co(A) the closed convex hull of the spectrum of A. An estimate for the norm of f(A) is obtained under the following conditions: f is a holomorphic function in a neighbourhood of co(A), and for some integer p the operator A p - ( A * ) p is Hilbert-Schmidt. The estimate improves one by I. Gelfand and G. Shilov.