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A characterization of polynomially Riesz strongly continuous semigroups

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

Commentationes Mathematicae Universitatis Carolinae

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.

A note on the commutator of two operators on a locally convex space

Edvard Kramar (2016)

Commentationes Mathematicae Universitatis Carolinae

Denote by C the commutator A B - B A of two bounded operators A and B acting on a locally convex topological vector space. If A C - C A = 0 , we show that C is a quasinilpotent operator and we prove that if A C - C A is a compact operator, then C is a Riesz operator.

Absolutely (r,p,q)-summing inclusions

Carsten Michels (2007)

Studia Mathematica

As a continuation of the work of Bennett and Carl for the case q = ∞, we consider absolutely (r,p,q)-summing inclusion maps between Minkowski sequence spaces, 1 ≤ p,q ≤ 2. Using these results we deduce parts of the limit orders of the corresponding operator ideals and an inclusion theorem between the ideals of (u,s,t)-nuclear and of absolutely (r,p,q)-summing operators, which gives a new proof of a result of Carl on Schatten class operators. Furthermore, we also consider inclusions between arbitrary...

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