Locally convex spaces. (English) Zbl 0466.46001

Jarchow, Hans

Mathematische Leitfäden. Stuttgart: B. G. Teubner. 548 p. DM 98.00 (1981).

MSC:

46-02	Research exposition (monographs, survey articles) pertaining to functional analysis
46A03	General theory of locally convex spaces
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.)
46-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to functional analysis
46M40	Inductive and projective limits in functional analysis
46A20	Duality theory for topological vector spaces
46A08	Barrelled spaces, bornological spaces
46A04	Locally convex Fréchet spaces and (DF)-spaces
46M05	Tensor products in functional analysis
46A30	Open mapping and closed graph theorems; completeness (including \(B\)-, \(B_r\)-completeness)
46A22	Theorems of Hahn-Banach type; extension and lifting of functionals and operators
47B10	Linear operators belonging to operator ideals (nuclear, \(p\)-summing, in the Schatten-von Neumann classes, etc.)
47L30	Abstract operator algebras on Hilbert spaces

Keywords:

projective and inductive limits; F-semi-norms; strictly webbed tvs; closed graph theorem; Hahn-Banach theorem; Klein-Milman theorem; duality; Stone-Weierstraß theorem; Schwartz spaces; diametral dimension; barrelledness; reflexivity; gDF-spaces; Prokhorov’s theorem; bornological and ultrabornological spaces; Nachbin-Shirota’s theorem; bases; Orlicz- Pettis theorem; tensor products; nuclearity; factorization theorem for weakly compact operators; approximation property; operator ideals; absolutely p-summing operators; strongly nuclear operators; Hilbert- Schmidt operators; Grothendieck inequality; Dunford-Pettis property; Choquet simplex