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Displaying similar documents to “On the orbits of an operator with spectral radius one”

On spectral representation for selfadjoint operators. Expansion in generalized eigenelements

Eberhard Gerlach (1965)

Annales de l'institut Fourier

Similarity:

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...

Compact AC-operators

Ian Doust, Byron Walden (1996)

Studia Mathematica

Similarity:

We prove that compact AC-operators have a representation as a combination of disjoint projections which mirrors that for compact normal operators. We also show that unlike arbitrary AC-operators, compact AC-operators admit a unique splitting into real and imaginary parts, and that these parts must necessarily be compact.

Spectral radius formula for commuting Hilbert space operators

Vladimír Muller, Andrzej Sołtysiak (1992)

Studia Mathematica

Similarity:

A formula is given for the (joint) spectral radius of an n-tuple of mutually commuting Hilbert space operators analogous to that for one operator. This gives a positive answer to a conjecture raised by J. W. Bunce in [1].