𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Separately continuous functions on products of locally convex spaces with the weak topology

✍ Scribed by V. V. Mikhailyuk

Publisher
Springer US
Year
1999
Tongue
English
Weight
337 KB
Volume
96
Category
Article
ISSN
1573-8795

No coin nor oath required. For personal study only.

📜 SIMILAR VOLUMES

The weak topology on q-convex Banach fun
The weak topology on q-convex Banach function spaces
✍ L. Agud; J. M. Calabuig; E. A. Sánchez Pérez 📂 Article 📅 2011 🏛 John Wiley and Sons 🌐 English ⚖ 198 KB 👁 1 views

## Abstract Let __X__(μ) be a Banach function space. In this paper we introduce two new geometric notions, __q__‐convexity and weak __q__‐convexity associated to a subset __S__ of the unit ball of the dual of __X__(μ), 1 ≤ __q__ < ∞. We prove that in the general case both notions are not equivalent

Integral functionals that are continuous
Integral functionals that are continuous with respect to the weak topology on
✍ Robert Černý; Stanislav Hencl; Jan Kolář 📂 Article 📅 2009 🏛 Elsevier Science 🌐 English ⚖ 685 KB

Let Ω ⊂ R N be a bounded open set and let g: Ω × R → R be a Carathéodory function that satisfies standard growth conditions. Then the functional Φ(u) = Ω g (x, u(x)) dx is weakly continuous on W 1,p 0 (Ω), 1 ≤ p ≤ ∞, if and only if g is linear in the second variable.