Description

This book presents a theory motivated by the spaces LP, 0 ≤ p < l. This book presents a theory motivated by the spaces LP, 0 ≤ p < l. These spaces are not locally convex, so the methods usually encountered in linear analysis (particularly the Hahn–Banach theorem) do not apply here. This book presents a theory motivated by the spaces LP, 0 ≤ p < l. These spaces are not locally convex, so the methods usually encountered in linear analysis (particularly the Hahn–Banach theorem) do not apply here. This book presents a theory motivated by the spaces LP, 0 ≤ p < l. These spaces are not locally convex, so the methods usually encountered in linear analysis (particularly the Hahn–Banach theorem) do not apply here. Questions about the size of the dual space are especially important in the non-locally convex setting, and are a central theme. Several of the classical problems in the area have been settled in the last decade, and a number of their solutions are presented here. The book begins with concrete examples (lp, LP, L0, HP) before going on to general results and important counterexamples. An F-space sampler will be of interest to research mathematicians and graduate students in functional analysis. 1. Preliminaries; 2. Some of the classic results; 3. Hardy spaces; 4. The Hahn-Banach extension property; 5. Three space problems; 6. Lifting Theorems; 7. Transitive spaces and small operators; 8. Operators between LP spaces; 9. Compact convex sets with no extreme points; 10. Notes on