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Displaying similar documents to “A characterization of polynomially Riesz strongly continuous semigroups”

Geometry of the spectral semidistance in Banach algebras

Gareth Braatvedt, Rudi Brits (2014)

Czechoslovak Mathematical Journal

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Let A be a unital Banach algebra over ℂ , and suppose that the nonzero spectral values of a and b ∈ A are discrete sets which cluster at 0 ∈ ℂ , if anywhere. We develop a plane geometric formula for the spectral semidistance of a and b which depends on the two spectra, and the orthogonality relationships between the corresponding sets of Riesz projections associated with the nonzero spectral values. Extending a result of Brits and Raubenheimer, we further show that a and b are quasinilpotent equivalent...

Riesz spaces of order bounded disjointness preserving operators

Fethi Ben Amor (2007)

Commentationes Mathematicae Universitatis Carolinae

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Let L , M be Archimedean Riesz spaces and ℒ b ( L , M ) be the ordered vector space of all order bounded operators from L into M . We define a Lamperti Riesz subspace of ℒ b ( L , M ) to be an ordered vector subspace ℒ of ℒ b ( L , M ) such that the elements of ℒ preserve disjointness and any pair of operators in ℒ has a supremum in ℒ b ( L , M ) that belongs to ℒ . It turns out that the lattice operations in any Lamperti Riesz subspace ℒ of ℒ b ( L , M ) are given pointwise, which leads to a generalization of the classic Radon-Nikod’ym theorem...

Sturm-Liouville systems are Riesz-spectral systems

Cédric Delattre, Denis Dochain, Joseph Winkin (2003)

International Journal of Applied Mathematics and Computer Science

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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.