L^p(G, X^*) comme sous-espace complémenté de L^q(G, X)^*

Abstract

Let G be a compact metric infinite abelian group and let X be a Banach space. We study the following question: if the dual X * of X does not have the Radon-Nikodym property, is L p (G, X * ) complemented in L q (G, X) * , 1 < p ≤ ∞, 1/p + 1/q = 1, or, if p = 1, in the subspace of C(G, X) * consisting of the measures that are absolutely continuous with respect to the Haar measure?We show that the answer is negative if X is separable and does not contain 1 , and if 1 ≤ p < ∞. If p = 1, this answers a question of G. Emmanuele. We show that the answer is positive if X * is a Banach lattice that does not contain a copy of c0, 1 ≤ p < ∞. It is also positive, by a different method, if p = ∞ and X * = M (K), where K is a compact space with a perfect subset.Moreover, we examine whether CΛ(G, X * ) may be complemented in L ∞ Λ (G, X * ), where Λ is a subset of Γ , the dual group of G, when the space X is separable and L 1 (G, X)/L 1 Λ c (G, X) does not contain 1 .

Magnetic biodegradable Fe3O4/CS/PVA nanofibrous membranes for bone regeneration

“…When the applied voltage increased to 25 kV, heterogeneous nanofibers were present again. The formation of beads may be ascribed to the instability of the jet at the spinning tip arising from lower voltage of 10 and 15 kV [4], while the relatively higher voltage (20 kV) could induce more charges to stretch the solution jet more easily and stably, which yield more uniform and smooth nanofibers [48][49][50]. The heterogeneity of nanofibers present at voltage of 25 kV is due to the fact that too high voltage will break the force balance and lead to the instability of Taylor cone, which was consequently dedicated to forming heterogeneous fiber.…”