Quantification of the reciprocal Dunford-Pettis property
We prove in particular that Banach spaces of the form C₀(Ω), where Ω is a locally compact space, enjoy a quantitative version of the reciprocal Dunford-Pettis property.
Quelques propriétés des espaces de Banach stables
Quelques remarques sur les opérateurs et les q-algèbres de Banach.
Quotients of Banach spaces and surjectively universal spaces
We characterize those classes 𝓒 of separable Banach spaces for which there exists a separable Banach space Y not containing ℓ₁ and such that every space in the class 𝓒 is a quotient of Y.
Quotients of Banach Spaces with the Daugavet Property
We consider a general concept of Daugavet property with respect to a norming subspace. This concept covers both the usual Daugavet property and its weak* analogue. We introduce and study analogues of narrow operators and rich subspaces in this general setting and apply the results to show that a quotient of L₁[0,1] by an ℓ₁-subspace need not have the Daugavet property. The latter answers in the negative a question posed to us by A. Pełczyński.
Quotients of Continuous Convex Functions on Nonreflexive Banach Spaces
On each nonreflexive Banach space X there exists a positive continuous convex function f such that 1/f is not a d.c. function (i.e., a difference of two continuous convex functions). This result together with known ones implies that X is reflexive if and only if each everywhere defined quotient of two continuous convex functions is a d.c. function. Our construction also gives a stronger version of Klee's result concerning renormings of nonreflexive spaces and non-norm-attaining functionals.
Quotients with a shrinking basis
We present a simple proof of a theorem that yields as a corollary a result of Valdivia that sharpens an old result of Johnson and Rosenthal.