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 . 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 and of with such that the part of the generator in is unbounded with resolvent of Riesz type while its part in is a polynomially Riesz operator.