拓扑向量空间(第2版)(英文影印版)

.5 projective topologies
6 inductive topologies
7 barreled spaces
8 bornological spaces
9 separation of convex sets
10 compact convex sets
exerises
iii. linear mappings introducction
1 continuous linear maps and topological homomorphisms
2 banach's homomorphism theorem
3 spaces of linear mappings
4 equicontinuity.the principle of uniform boundedness and the banach-steinhaus theorem
5 bilinear mappings
6 topological tensor products
7 nuclear mappings and spaces
8 examples of nuclear spaces
9 the approximation property.compact maps
exercises
iv. duality introducction
1 dual systems and weak topologies
2 elementary properties of adjoint maps
3 locally convex topologies consistent with a given duality.the mackey-arens theorem
4 duality of projective and inductive topologies
5 strong dual of a localy convex space.bidual.reflexive spaces
6 dual characterization of completeness,metrizable spaces.theorems of grothendieck,banach-dieudonne,and krein-smulian
7 adjoints of closed linear mappings..
8 the general open mapping and closed graph theorems
9 tensor products and nuclear spaces
10 nuclear spaces and absolute summability
11 weak compactness. theorems of eberlein and krein
exercises
v.order structures
introduction
1 ordered vector spaces over the real field
2 ordered vector spaces over the complex field
3 duality of convex cones
4 ordered topological vector spaces
5 positive linear forms and mappings
6 the order topology
7 topological vector lattices
8 continuous functions on a compact space. theorems
of stone-weierstrass and kakutani
exercises
vi. c*-and w*-algebras
introduction
1 preliminaries
2 c*-algebras. the gelfand theorem
3 order structure of a c*-algebra
4 positive linear forms. representations
s projections and extreme points
6 w*-algebras
7 von neumann algebras. kaplansky's density theorem
8 projecdons and types of w*-algebras
exercises
appendix. spectral properties of positive operators
introduction
1 elementary properties of the resolvent
2 pringshelm's theorem and its consequences
table of contents
3 the peripheral point spectrum
index of symbols
bibliography
index...