Topological Vector Spaces II

Cover
Title page
CHAPTER SEVEN: Linear Mappings and Duality
32. Homomorphisms of locally convex spaces
1. Weak continuity
2. Continuity
3. Weak homomorphisms
4. The homomorphism theorem
5. Further results on homomorphisms
33. Linear continuous mappings of (B)- and (F)-spaces
1. First results in normed spaces
2. Metrizable locally convex spaces
3. Applications of the BANACH-DIEUDONNÉ theorem
4. Homomorphisms in (B)- and (F)-spaces
5. Separability. A theorem of SOBCZYK
6. (FM)-spaces
34. The theory of PTAK
1. Nearly open mappings
2. PTAK spaces and the BANACH-SCHAUDER theorem
3. Some results on PTAK spaces
4. A theorem of KELLEY
5. Closed linear mappings
6. Nearly continuous mappings and the c1osed-graph theorem
7. Some consequences, the HELLINGER-TOEPLITZ theorem
8. The theorems of A. and W. ROBERTSON
9. The closed-graph theorem of KOMURA
10. The open mapping theorem of ADASCH
11 KALTON'S c1osed-graph theorems
35. DE WILDE'S theory
1. Webs in locally convex spaces
2. The closed-graph theorems of DE WILDE
3. The corresponding open-mapping theorems
4 Hereditary properties of webbed and strictly webbed spaces
5. A generalization of the open-mapping theorem
6. The localization theorem for strictly webbed spaces
7. Ultrabornological spaces and fast convergence
8. The associated ultrabornological space
9. Infra-(u)-spaces
10. Further results
36. Arbitrary linear mappings
1. The singularity of a linear mapping
2. Some examples
3. The adjoint mapping
4. The contraction of A
5. The adjoint of the contraction
6. The second adjoint
7. Maximal mappings
8. Dense maximal mappings
37. The graph topology. Open mappings
1. The graph topology
2. The adjoint of AI_A
3. Nearly open mappings
4. Open mappings
5. PTAK spaces. Open mapping theorems
6. Linear mappings in metrizable spaces
7. Open mappings in (B)- and (F)-spaces
8. Domains and ranges of closed mappings of (F)-spaces
38. Linear equations and inverse mappings
1. Solvability conditions
2. Continuous left and right inverses
3. Extension and lifting properties
4. Inverse mappings
5. Solvable pairs of mappings
6. Infinite systems of linear equations
CHAPTER EIGHT: Spaces of Linear and Bilinear Mappings
39. Spaces of linear mappings
1. Topologies on L(E,F)
2. The BANACH-MACKEY theorem
3. Equicontinuous sets
4. Weak compactness. Metrizability
5. The BANACH-STEINHAUS theorem
6. Completeness
7. The dual of L_s(E,F)
8. Some structure theorems
40. Bilinear mappings
1. Fundamental notions
2. Continuity theorems for bilinear maps
3. Extensions of bilinear mappings
4. Locally convex spaces of bilinear mappings
5. Applications. Locally convex algebras
41. Projective tensor products of locally convex spaces
1. Some complements on tensor products
2. The projective tensor product
3. The dual space. Representations of E?F
4. The projective tensor product of metrizable and of (DF)-spaces
5. Tensor products of linear maps
6. Further hereditary properties
7. Some special cases
42. Compact and nuclear mappings
1. Compact linear mappings
2. Weakly compact linear mappings
3. Completely continuous mappings. Examples
4. Compact mappings in Hilbert space
5. Nuc1ear mappings
6. Examples of nuc1ear mappings
7. The trace
8. Factorization of compact mappings
9. Fixed points and invariant subspaces
43. The approximation property
1. Some basic results
2. The canonical map of E?F in B(E'_sx F'_s)
3. Another interpretation of the approximation property
4. Hereditary properties
5. Bases, Schauder bases, weak bases
6. The basis problem
7. Some function spaces with the approximation property
8. The bounded approximation property
9. Johnson's universal space
44. The injective tensor product and the ε-product
1. Compatible topologies on E?F
2. The injective tensor product
3. Relatively compact subsets of EεF and E?F
4. Tensor products of mappings
5. Hereditary properties
6. Further results on tensor product mappings
7. Vector valued continuous functions
8. ε-tensor product with a sequence space
45. Duality of tensor products
1. First results
2. A theorem of SCHATTEN
3. BUCHWALTER's results on duality
4. Canonical representations of integral bilinear forms
5. Integral mappings
6. Nuc1ear and integral norms
7. When is every integral mapping nuc1ear?
Bibliography
Author and Subject Index