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  3. An F-space Sampler
  • Cited by 180
Publisher:
Cambridge University Press
Online publication date:
October 2013
Print publication year:
1984
Online ISBN:
9780511662447
DOI:
https://doi.org/10.1017/CBO9780511662447
Subjects:
Mathematics (general), Mathematics, Abstract Analysis
Series:
London Mathematical Society Lecture Note Series (89)
Information

Book description

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.

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