In the preface to Volume One I promised a second volume which would contain the theory of linear mappings and special classes of spaces imยญ portant in analysis. It took me nearly twenty years to fulfill this promise, at least to some extent. To the six chapters of Volume One I added two new chapters, one on linear mappings and duality (Chapter Seven), the second on spaces of linear mappings (Chapter Eight). A glance at the Contents and the short introductions to the two new chapters will give a fair impression of the material included in this volume. I regret that I had to give up my intention to write a third chapter on nuclear spaces. It seemed impossible to include the recent deep results in this field without creating a great further delay. A substantial part of this book grew out of lectures I held at the Mathematics Department of the University of Marylandยท during the academic years 1963-1964, 1967-1968, and 1971-1972. I would like to express my gratitude to my colleagues J. BRACE, S. GOLDBERG, J. HORVATH, and G. MALTESE for many stimulating and helpful discussions during these years. I am particularly indebted to H. JARCHOW (Ziirich) and D. KEIM (Frankfurt) for many suggestions and corrections. Both have read the whole manuscript. N. ADASCH (Frankfurt), V. EBERHARDT (Miinchen), H. MEISE (Diisseldorf), and R. HOLLSTEIN (Paderborn) helped with important observations
CONTENT
of Vol. II -- Seven Linear Mappings and Duality -- ยง32. Homomorphisms of locally convex spaces -- ยง33. Linear continuous mappings of (B)-and (F)-spaces -- ยง34. The theory of Ptรกk -- ยง35. De Wildeโs theory -- ยง36. Arbitrary linear mappings -- ยง37. The graph topology. Open mappings -- ยง38. Linear equations and inverse mappings -- Eight Spaces of Linear and Bilinear Mappings -- ยง39. Spaces of linear mappings -- ยง40. Bilinear mappings -- ยง41. Projective tensor products of locally convex spaces -- ยง42. Compact and nuclear mappings -- ยง43. The approximation property -- ยง44. The injective tensor product and the ?-product -- ยง45. Duality of tensor products -- Author and Subject Index
