of Vol. II.- 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 Pták.- 1. Nearly open mappings.- 2. Pták spaces and the Banach-Schauder theorem.- 3. Some results on Pták spaces.- 4. A theorem of Kelley.- 5. Closed linear mappings.- 6. Nearly continuous mappings and the closed-graph theorem.- 7. Some consequences, the Hellinger-Toeplitz theorem.- 8. The theorems of A. and W. Robertson.- 9. The closed-graph theorem of Kömura.- 10. The open mapping theorem of Adasch.- 11. Kalton’s closed-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 AIA.- 3. Nearly open mappings.- 4. Open mappings.- 5. Pták 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.- 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 Ls (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. Nuclear mappings.- 6. Examples of nuclear 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?s × 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 ?-product.- 1. Compatible topologies on E ? F.- 2. The injective tensor product.- 3. Relatively compact subsets of E?F and E ???F.- 4. Tensor products of mappings.- 5. Hereditary properties.- 6. Further results on tensor product mappings.- 7. Vector valued continuous functions.- 8. ?-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. Nuclear and integral norms.- 7. When is every integral mapping nuclear?.- Author and Subject Index.
