Author | Schatten, Robert. author |
---|---|
Title | Norm Ideals of Completely Continuous Operators [electronic resource] / by Robert Schatten |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg, 1960 |
Connect to | http://dx.doi.org/10.1007/978-3-642-87652-3 |
Descript | VIII, 83 p. online resource |
Preliminaries and notation -- I. The class of operators of the form ?j?j ?j ? ??j -- 1. The operator ?j ?j ?j ? ??j -- 2. The spectrum of the operator ?j ?j ?j ? ??j -- 3. Completely continuous operators -- 4. The spectral representation of a completely continuous Hermitean operator -- 5. Some equalities and inequalities for the proper values of completely continuous Hermitean operators -- 6. Some ideals of operators -- 7. The ideals of completely continuous operators -- 8. Some uniformly closed left ideals of completely continuous operators -- II. The Schmidt-class -- 1. (? c) as a Hilbert space of completely continuous operators -- 2. The Schmidt-class of operators on L2 -- III. The trace-class -- 1. (? c) as a Banach space of completely continuous operators -- 2. A maximum problem in (? c) -- IV. The successive conjugate spaces of the space ? of all completely continuous operators -- 1. A characterization of ?* and ?** -- 2. ? is not a conjugate space -- 3. Some linear functionals on the space of all operators -- V. Norm ideals -- 1. Crossnorms and norm ideals -- 2. A maximum problem for ?n -- 3. Symmetric gauge functions on