Finite representability of the Yang operator.
Tauberian operators on spaces
We characterize tauberian operators in terms of the images of disjoint sequences and in terms of the image of the dyadic tree in . As applications, we show that the class of tauberian operators is stable under small norm perturbations and that its perturbation class coincides with the class of all weakly precompact operators. Moreover, we prove that the second conjugate of a tauberian operator is also tauberian, and the induced operator is an isomorphism into. Also, we show that embeds...
Local dual spaces of a Banach space
We study the local dual spaces of a Banach space X, which can be described as the subspaces of X* that have the properties that the principle of local reflexivity attributes to X as a subspace of X**. We give several characterizations of local dual spaces, which allow us to show many examples. Moreover, every separable space X has a separable local dual Z, and we can choose Z with the metric approximation property if X has it. We also show that a separable space containing no...
Tauberian operators on spaces of integrable functions.
Quotients of L by reflexive subspaces.
Here we present and example and some results suggesting that there is no infinite-dimensional reflexive subspace Z of L1 ≡ L1[0,1] such that the quotient L1/Z is isomorphic to a subspace of L1.
Rosenthal and semi-Tauberian linear relations in normed spaces
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...
Representation of operators with martingales and the Radon-Nikodým property.
The Radon-Nikodým property was introduced to describe those Banach spaces X for which all operators acting between L1 and X have a representation function. These spaces can be characterized in terms of martingales, as those spaces in which every uniformly bounded martingale converges. In the present work we study some classes of operators defined upon their behaviour with respect to the convergence of such martingales. We prove that an operator preserves the non-convergence of uniformly bounded...
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...
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