Topological vector spaces. 4th corr. printing. (English) Zbl 0435.46003

Schaefer, Helmut H.

Graduate Texts in Mathematics, 3. New York-Heidelberg-Berlin: Springer-Verlag. XI, 294 p. DM 48.00; $ 28.40 (1980).

MSC:

46A03	General theory of locally convex spaces
46-02	Research exposition (monographs, survey articles) pertaining to functional analysis
46A04	Locally convex Fréchet spaces and (DF)-spaces
46A20	Duality theory for topological vector spaces
46A30	Open mapping and closed graph theorems; completeness (including \(B\)-, \(B_r\)-completeness)
46A32	Spaces of linear operators; topological tensor products; approximation properties
46A25	Reflexivity and semi-reflexivity
46A40	Ordered topological linear spaces, vector lattices
46B42	Banach lattices
46A55	Convex sets in topological linear spaces; Choquet theory
47B60	Linear operators on ordered spaces
46F05	Topological linear spaces of test functions, distributions and ultradistributions
46A13	Spaces defined by inductive or projective limits (LB, LF, etc.)
46A11	Spaces determined by compactness or summability properties (nuclear spaces, Schwartz spaces, Montel spaces, etc.)

Keywords:

convex; Hahn Banach theorem; locally convex spaces; projective topologies; inductive topologies; barreled spaces; bornological spaces; Banach’s homomorphism theorem; spaces of linear mappings; equicontinuity; uniform boundedness; Banach-Steinhaus theorem; tensor products; nuclear mappings and spaces; Mackey-Arens theorem; reflexive spaces; theorems of Grothendieck, Banach-Dieudonné, and Krein-Šmulian; open mapping and closed graph theorems; absolute summability; theorems of Eberlein and Krein; convex cones; ordered topological vector spaces; theorems of Stone-Weierstrass and Kakutani; positive operators

Citations:

Zbl 0141.305