On the subspaces of JF and JT with non-separable dual

Abstract

The connectivity of the hydrophobic medium in the nonionic binary system C 12 EO 6 /H 2 O is studied by monitoring the diffusion constants of tracer molecules at the transition between the hexagonal mesophase and the fluid isotropic phase. The increase in the transverse diffusion coefficient on approaching the isotropic phase reveals the proliferation of bridge-like defects connecting the surfactant cylinders. This suggests that the isotropic phase has a highly connected structure. Indeed, we find similar diffusion coefficients in the isotropic and cubic bicontinuous phases. The temperature dependence of the lattice parameter in the hexagonal phase confirms the change in connectivity close to the hexagonal-isotropic transition. Finally, an X-ray investigation of the isotropic phase shows that its structure is locally similar to that of the hexagonal phase.

Hausdorff measures and functions of bounded quadratic variation

“…In our previous work (cf. [1]), but also in [3], we have started studying the structure of the subspaces of V 0 2 . ¿From our point of view a sufficient understanding of the structure of V 0 2 requires answers to the following problems.…”

“…To see this we start with some f ∈ X * * \ X, where X * * is considered as a subspace of V 2 . Since X does not contain ℓ 1 Odell-Rosenthal's theorem (cf. [18]) yields that there exists a bounded sequence (f n ) n in X pointwise converging to f .…”

Unconditional families in Banach spaces

“…This result reveals the generic character of the basis of the James Tree space J T , the first example of a separable Banach space not containing 1 and with non-separable dual [21]. For further applications of Theorem 1 we refer to [1].…”

“…Using (c) above and properties (1) and (4) of Theorem 10, we see that for every σ ∈ 2 N the sequence (e σ |n ) n is weak* convergent to the element…”

“…For further applications of Theorem 1 we refer to [1]. The ingredients for proving Theorem 1 are mainly Ramsey theoretical.…”