Quelques propriétés des modèles étalés sur les espaces de Banach
Quelques propriétés des opérateurs uniformément convexifiants
Quelques propriétés measurables de diverses suites d'un espace de Banach séperable E dans E...
Quelques remarques sur la propriété (C) des espaces de Banach
Quelques remarques sur les opérateurs et les q-algèbres de Banach.
Quelques résultats concernant l'inconditionnalité
Quotients and interpolation spaces of stable Banach spaces
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 of indecomposable Banach spaces of continuous functions
Assuming ⋄, we construct a connected compact topological space K such that for every closed L ⊂ K the Banach space C(L) has few operators, in the sense that every operator on C(L) is multiplication by a continuous function plus a weakly compact operator. In particular, C(K) is indecomposable and has continuum many non-isomorphic indecomposable quotients, and K does not contain a homeomorphic copy of βℕ. Moreover, assuming CH we construct a connected compact K where C(K) has few...
Quotients of for 0 ≤ p < 1
Quotients of L1 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.
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.
Rademacher functions in BMO
The Rademacher sums are investigated in the BMO space on [0,1]. They span an uncomplemented subspace, in contrast to the dyadic space on [0,1], where they span a complemented subspace isomorphic to l₂. Moreover, structural properties of infinite-dimensional closed subspaces of the span of the Rademacher functions in BMO are studied and an analog of the Kadec-Pełczyński type alternative with l₂ and c₀ spaces is proved.
Rademacher functions in Cesàro type spaces
The Rademacher sums are investigated in the Cesàro spaces (1 ≤ p ≤ ∞) and in the weighted Korenblyum-Kreĭn-Levin spaces on [0,1]. They span l₂ space in for any 1 ≤ p < ∞ and in if and only if the weight w is larger than on (0,1). Moreover, the span of the Rademachers is not complemented in for any 1 ≤ p < ∞ or in for any quasi-concave weight w. In the case when p > 1 and when w is such that the span of the Rademacher functions is isomorphic to l₂, this span is a complemented...
Rademacher functions in weighted Cesàro spaces
We study the behaviour of the Rademacher functions in the weighted Cesàro spaces Ces(ω,p), for ω(x) a weight and 1 ≤ p ≤ ∞. In particular, the case when the Rademacher functions generate in Ces(ω,p) a closed linear subspace isomorphic to ℓ² is considered.
Rademacher series and decoupling.
Rademacher series from Orlicz to the present day
We survey some questions on Rademacher series in both Banach and quasi-Banach spaces which have been the subject of extensive research from the time of Orlicz to the present day.
Rademacher variables in connection with complex scalars.