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Rosenthal and semi-Tauberian linear relations in normed spaces

Teresa Álvarez, Antonio Martínez-Abejón (2005)

Bollettino dell'Unione Matematica Italiana

The class of Rosenthal linear relations in normed spaces is introduced and studied in terms of their first and second conjugates. We investigate the relationship between a Rosenthal linear relation and its conjugate. In this paper, we also study the semi-Tauberian linear relations following the pattern followed for the study of the Tauberian linear relations. We prove that the semi-Tauberian linear relations share some of the properties of Tauberian linear relations and they are related to Rosenthal...

Scattered elements of Banach algebras

Peng Cao (2013)

Studia Mathematica

A scattered element of a Banach algebra is an element with at most countable spectrum. The set of all scattered elements is denoted by (). The scattered radical s c ( ) is the largest ideal consisting of scattered elements. We characterize in several ways central elements of modulo the scattered radical. As a consequence, it is shown that the following conditions are equivalent: (i) () + () ⊂ (); (ii) ()() ⊂ (); (iii) [ ( ) , ] s c ( ) .

Sturm-Liouville systems are Riesz-spectral systems

Cédric Delattre, Denis Dochain, Joseph Winkin (2003)

International Journal of Applied Mathematics and Computer Science

The class of Sturm-Liouville systems is defined. It appears to be a subclass of Riesz-spectral systems, since it is shown that the negative of a Sturm-Liouville operator is a Riesz-spectral operator on L^2(a,b) and the infinitesimal generator of a C_0-semigroup of bounded linear operators.

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