All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 5

Displaying 81 – 92 of 92

Showing per page

Operator ideal properties of vector measures with finite variation

Susumu Okada, Werner J. Ricker, Luis Rodríguez-Piazza (2011)

Studia Mathematica

Given a vector measure m with values in a Banach space X, a desirable property (when available) of the associated Banach function space L¹(m) of all m-integrable functions is that L¹(m) = L¹(|m|), where |m| is the [0,∞]-valued variation measure of m. Closely connected to m is its X-valued integration map Iₘ: f ↦ ∫f dm for f ∈ L¹(m). Many traditional operators from analysis arise as integration maps in this way. A detailed study is made of the connection between the property L¹(m) = L¹(|m|) and the...

Operator semigroups in Banach space theory

Pietro Aiena, Manuel González, Antonio Martínez-Abejón (2001)

Bollettino dell'Unione Matematica Italiana

In questo lavoro, motivati dalla teoria di Fredholm in spazi di Banach e dalla cosiddetta teoria degli ideali di operatori nel senso di Pietsch, viene definito un nuovo concetto di semigruppo di operatori. Questa nuova definizione include quella di molte classi di operatori già studiate in letteratura, come la classe degli operatori di semi-Fredholm, quella degli operatori tauberiani ed altre ancora. Inoltre permette un nuovo ed unificante approccio ad una serie di problemi in teoria degli operatori...

Operator theoretic properties of semigroups in terms of their generators

S. Blunck, L. Weis (2001)

Studia Mathematica

Let ( T t ) be a C₀ semigroup with generator A on a Banach space X and let be an operator ideal, e.g. the class of compact, Hilbert-Schmidt or trace class operators. We show that the resolvent R(λ,A) of A belongs to if and only if the integrated semigroup S t : = ∫ 0 t T s d s belongs to . For analytic semigroups, S t ∈ implies T t ∈ , and in this case we give precise estimates for the growth of the -norm of T t (e.g. the trace of T t ) in terms of the resolvent growth and the imbedding D(A) ↪ X.

Operators whose adjoints are quasi p-nuclear

J. M. Delgado, C. Piñeiro, E. Serrano (2010)

Studia Mathematica

For p ≥ 1, a set K in a Banach space X is said to be relatively p-compact if there exists a p-summable sequence (xₙ) in X with K ⊆ ∑ ₙ α ₙ x ₙ : ( α ₙ ) ∈ B ℓ p ' . We prove that an operator T: X → Y is p-compact (i.e., T maps bounded sets to relatively p-compact sets) iff T* is quasi p-nuclear. Further, we characterize p-summing operators as those operators whose adjoints map relatively compact sets to relatively p-compact sets.

Orbits in symmetric spaces, II

N. J. Kalton, F. A. Sukochev, D. Zanin (2010)

Studia Mathematica

Suppose E is fully symmetric Banach function space on (0,1) or (0,∞) or a fully symmetric Banach sequence space. We give necessary and sufficient conditions on f ∈ E so that its orbit Ω(f) is the closed convex hull of its extreme points. We also give an application to symmetrically normed ideals of compact operators on a Hilbert space.

Currently displaying 81 – 92 of 92

Previous Page 5