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Automatic continuity of linear operators

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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.

Author(s): Allan M. Sinclair
Series: London Mathematical Society Lecture Note Series
Publisher: CUP
Year: 1976

Language: English
Pages: 98

Contents......Page 5
Introduction......Page 7
1. The separating space......Page 13
2. Discontinuity points......Page 20
2. Intertwining operators......Page 25
4. When R has countable spectrum......Page 30
5. Operators intertwining with normal operators......Page 33
3. Homomorphisms......Page 38
6. Isomorphisms of semisimple Banach algebras......Page 39
7. Ring isomorphisms of semisimple Banach algebras......Page 50
8. Existence of discontinuous homomorphisms and derivations......Page 54
9. Homomorphisms between C(Omega)- modules......Page 60
10. Homomorphisms from C(Omega)......Page 64
11. Homomorphisms into radical Banach algebras......Page 68
12. Homomorphisms and derivations from C^*-algebras......Page 74
13. Positive linear functionals......Page 79
Bibliography......Page 86
Index......Page 96