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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.

Function spaces. --- Metric spaces. --- Spaces, Metric --- Generalized spaces --- Set theory --- Topology --- Spaces, Function --- Functional analysis

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Analytical spaces --- Banach spaces --- Sequences (Mathematics) --- Series --- Banach, Espaces de --- Suites (Mathématiques) --- Séries (Mathématiques) --- Sequence (Mathematics) --- 517.984 --- Algebra --- Mathematics --- Processes, Infinite --- Mathematical sequences --- Numerical sequences --- Functions of complex variables --- Generalized spaces --- Topology --- Spectral theory of linear operators --- 517.984 Spectral theory of linear operators --- Suites (Mathématiques) --- Séries (Mathématiques) --- Analyse fonctionnelle --- Functional analysis --- Functional analysis. --- Espaces de banach --- Suites et series

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Algebra's [Lineaire ] --- Algebras [Linear ] --- Algèbres linéaires --- Anneaux commutatifs --- Commutatieve ringen --- Commutative rings --- Lineaire algebra's --- Linear algebras --- Algebras, Linear --- 512.64 --- Rings (Algebra) --- Linear algebra --- Algebra, Universal --- Generalized spaces --- Mathematical analysis --- Calculus of operations --- Line geometry --- Topology --- Linear and multilinear algebra. Matrix theory --- 512.64 Linear and multilinear algebra. Matrix theory

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The basic goals of the book are: (i) to introduce the subject to those interested in discovering it, (ii) to coherently present a number of basic techniques and results, currently used in the subject, to those working in it, and (iii) to present some of the results that are attractive in their own right, and which lend themselves to a presentation not overburdened with technical machinery.

Differential equations, Partial. --- Eigenvalues. --- Geometry, Riemannian. --- Riemann geometry --- Riemannian geometry --- Generalized spaces --- Geometry, Non-Euclidean --- Semi-Riemannian geometry --- Matrices --- Partial differential equations --- Differential equations, Partial --- Eigenvalues --- Geometry, Riemannian --- Equations aux dérivées partielles --- Valeurs propres --- Riemann, Géométrie de