An F-space Sampler
An F-space Sampler by N. J. Kalton, N. T. Peck, James W. Roberts
Publisher: Cambridge University Press | 1985 | ISBN: 0521275857 | 256 pages | PDF (scan) | 9,3 MB
Publisher: Cambridge University Press | 1985 | ISBN: 0521275857 | 256 pages | PDF (scan) | 9,3 MB
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.