Automatic Continuity of Linear Operators de Allan M. Sinclair

Automatic Continuity of Linear Operators: London Mathematical Society Lecture Note Series, cartea 21

Allan M. Sinclair

en Limba Engleză Paperback – 18 feb 1976

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.

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Cuprins

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(Ω)-modules; 10. Homomorphisms from C(Ω); 11. Homomorphisms into radical Banach algebras; 12. Homomorphisms and derivations from C*-algebras; Part IV: Linear Operators: 13. Positive linear functionals; Bibliography; Index.