An F-space Sampler (london Mathematical Society Lecture Note Series)
by N. J. Kalton /
1985 / English / PDF
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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.
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.
