Norm Ideals Of Completely Continuous Operators (ergebnisse Der Mathematik Und Ihrer Grenzgebiete Neue Folge Heft 27)

Contents: Preliminaries and notation. . . 1. The class of operators of the form 1: j Aj Cfj @ 1pj 7 1. The opera tor 1: j Aj Cfj @ 'lfJj ' . . . . . 7 2. The spectrum of the operator 1: j Aj Cfj @ (fj 10 3. Completely continuous operators . . . . . 12 4. The spectral representation of a completely continuous Hermitean operator . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 5. Some equalities and inequalities for the proper values of completely continuous Hermitean operators. . . . . . . . . . 21 6. Some ideals of operators . . . . . . . . . . . . . . . . . . . . 23 7. The ideals of completely continuous operators ...... . 25 8. Some uniformly closed left ideals of completely continuous operators 27 II. The Schmidt-class . . . . . . . . . . . . . . . . . . . 29 1. (a c) as a Hilbert space of completely continuous operators 29 2. The Schmidt-class of operators on L2. 34 III. The trace-class . . . . . . . . . . . . 36 1. (T c) as a Banach space of completely continuous operators 36 2. A maximum problem in ('r c) . . . . . . . . . . . . . 43 IV. The successive conjugate spaces of the space