On triangularization of algebras of operators.
On truncations of Hankel and Toeplitz operators.
We study the boundedness properties of truncation operators acting on bounded Hankel (or Toeplitz) infinite matrices. A relation with the Lacey-Thiele theorem on the bilinear Hilbert transform is established. We also study the behaviour of the truncation operators when restricted to Hankel matrices in the Schatten classes.
On weak (r,2)-summing operators and weak Hilbert spaces
On -nuclearity
One criterion for nuclearity of linear operators.
Operadores antisimétricos y de rango finito en espacios de Hilbert.
Opérateurs se factorisant par un espace , d’après S. Kwapien (suite et fin)
Opérateurs se factorisant par un espace , d’après S. Kwapien
Opérateurs sommants et factorisations. A travers les espaces
Opérateurs sommants sur un cone normal d un espace de Banach.
The aim of this paper is to develop a theory of p-summing operators (between Banach spaces) in presence of an order structure given by a convex normal cone.
Operational quantities derived from the norm and generalized Fredholm theory
We introduce and study some operational quantities associated to a space ideal . These quantities are used to define generalized semi-Fredholm operators associated to , and the corresponding perturbation classes which extend the strictly singular and strictly cosingular operators, and we study the generalized Fredholm theory obtained in this way. Finally we present some examples and show that the classes of generalized semi-Fredholm operators are non-trivial for several classical space ideals.
Operator ideal properties of vector measures with finite variation
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 norm inequalities of Minkowski type.
Operator semigroups in Banach space theory
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
Let 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 belongs to . For analytic semigroups, implies , and in this case we give precise estimates for the growth of the -norm of (e.g. the trace of ) in terms of the resolvent growth and the imbedding D(A) ↪ X.
Operatori di Riesz generalizzati su spazi di Banach
Operators whose adjoints are quasi p-nuclear
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 . 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.
Operators whose tensor powers are --continuous
Operators with Absolutely Bounded Matrices.
Orbits in symmetric spaces, II
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.