Norm Ideals of Completely Continuous Operators

Cover......Page 1
Title......Page 3
Preface......Page 5
Contents......Page 7
Preliminaries and notation......Page 9
1. The operator......Page 15
2. The spectrum of the operator......Page 18
3. Completely continuous operators......Page 20
4. The spectral representation of a completely continuous Hermitean operator......Page 22
5. Some equalities and inequalities for the proper values of completely continuous Hermitean operators......Page 29
6. Some ideals of operators......Page 31
7. The ideals of completely continuous operators......Page 33
8. Some uniformly closed left ideals of completely continuous operators......Page 35
1. (a c) as a Hubert space of completely continuous operators......Page 37
2. The Schmidt-class of operators on L2.......Page 42
1.  as a Banach space of completely continuous operators......Page 44
2. A maximum problem in......Page 51
1. A characterization of and......Page 53
2. C is not a conjugate space......Page 56
3. Some linear functionals on the space of all operators ......Page 58
1. Crossnorms and norm ideals......Page 62
2. A maximum problem for Rn......Page 66
3. Symmetric gauge functions on ?n .......Page 69
4. The unitarily invariant crossnorms on Rn ......Page 72
5. The symmetric gauge functions on 2 and the unitarily invariant cross-norms on R......Page 75
6. A special class of symmetric gauge functions......Page 79
7. Norm ideals and the minimal norm ideals......Page 81
8. The uniqueness of norm for the minimal norm ideals ......Page 86
9. An open problem......Page 87
Bibliography......Page 88