Displaying similar documents to “Sturm-Liouville systems are Riesz-spectral systems”

Continuity versus boundedness of the spectral factorization mapping

Holger Boche, Volker Pohl (2008)

Studia Mathematica

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This paper characterizes the Banach algebras of continuous functions on which the spectral factorization mapping 𝔖 is continuous or bounded. It is shown that 𝔖 is continuous if and only if the Riesz projection is bounded on the algebra, and that 𝔖 is bounded only if the algebra is isomorphic to the algebra of continuous functions. Consequently, 𝔖 can never be both continuous and bounded, on any algebra under consideration.

On strongly stable approximations.

F. Arandiga, V. Caselles (1994)

Revista Matemática de la Universidad Complutense de Madrid

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In this paper we prove that the convergence of (T - T)T to zero in operator norm (plus some technical conditions) is a sufficient condition for T to be a strongly stable approximation to T, thus extending some previous results existing in the literature.

A characterization of polynomially Riesz strongly continuous semigroups

Khalid Latrach, Martin J. Paoli, Mohamed Aziz Taoudi (2006)

Commentationes Mathematicae Universitatis Carolinae

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In this paper we characterize the class of polynomially Riesz strongly continuous semigroups on a Banach space X . Our main results assert, in particular, that the generators of such semigroups are either polynomially Riesz (then bounded) or there exist two closed infinite dimensional invariant subspaces X 0 and X 1 of X with X = X 0 ⊕ X 1 such that the part of the generator in X 0 is unbounded with resolvent of Riesz type while its part in X 1 is a polynomially Riesz operator.