Automatic Continuity of Linear Operators [Paperback]

Some of the results on automatic continuity of intertwining operators and homomorphisms that were obtained between 1960 and 1973 are collected here.Some of the results on automatic continuity of intertwining operators and homomorphisms that were obtained between 1960 and 1973 are here collected together to provide a detailed discussion of the subject. The book will be appreciated by graduate students of functional analysis who already have a good foundation in this and in the theory of Banach algebras.Some of the results on automatic continuity of intertwining operators and homomorphisms that were obtained between 1960 and 1973 are here collected together to provide a detailed discussion of the subject. The book will be appreciated by graduate students of functional analysis who already have a good foundation in this and in the theory of Banach algebras.Some of the results on automatic continuity of intertwining operators and homomorphisms that were obtained between 1960 and 1973 are here collected together to provide a detailed discussion of the subject. The book will be appreciated by graduate students of functional analysis who already have a good foundation in this and in the theory of Banach algebras.Introduction; Part I. Technical Results: 1. The separating space; 2. Discontinuity points; Part II. Intertwining Operators: 3. The existence of discontinuous intertwining operators; 4. When R has countable spectrum; 5. Operators intertwining with normal operators; Part III. Homomorphisms: 6. Isomorphisms of semisimple Banach algebras; 7. Ring isomorphisms of semisimple Banach algebras; 8. Existence of discontinuous homomorphisms and derivations; 9. Homomorphisms between C(?)-modules; 10. Homomorphisms from C(?); 11. Homomorphisms into radical Banach algebras; 12. Homomorphisms and derivations from C*-algebras; Part IV: Linear Operators: 13. Positive linear functionals; Bibliography; Index.