𝔖 Bobbio Scriptorium
✦   LIBER   ✦

AB-5* and Linear Compactness

✍ Scribed by Pham Ngoc Ánh; Dolors Herbera; Claudia Menini

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
231 KB
Volume
200
Category
Article
ISSN
0021-8693

No coin nor oath required. For personal study only.

✦ Synopsis

It is well known that there is a close relation between linear compactness and the Grothendieck condition AB-5*. In fact, for any cocomplete abelian category these conditions are equivalent to the exactness of inverse limits. However, the module categories are not selfdual and therefore Ž . these conditions are, in general, not equivalent for a given fixed module. In this paper, we emphasize the difference between these two important properties and show that in general, a ''proper'' condition AB-5* on a module M, i.e., M has AB-5*, but it is not linearly compact, is a very strong requirement on M.

📜 SIMILAR VOLUMES

Local compactness for linear elasticity
Local compactness for linear elasticity in irregular domains
✍ Norbert Weck 📂 Article 📅 1994 🏛 John Wiley and Sons 🌐 English ⚖ 278 KB

## Abstract For the theory of boundary value problems in linear elasticity, it is of crucial importance that the space of vector‐valued __L__^2^‐functions whose symmetrized Jacobians are square‐integrable should be compactly embedded in __L__^2^. For regions with the cone property this is usually a