Norm Ideals of Completely Continuous Operators

Norm Ideals of Completely Continuous Operators

by Robert Schatten

Paperback(Softcover reprint of the original 1st ed. 1960)

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Product Details

ISBN-13: 9783642876547
Publisher: Springer Berlin Heidelberg
Publication date: 04/05/2012
Series: Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge , #27
Edition description: Softcover reprint of the original 1st ed. 1960
Pages: 83
Product dimensions: 6.10(w) x 9.25(h) x 0.01(d)

Table of Contents

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 𝔄n.- 4. The unitarily invariant crossnorms on ?n.- 5. The symmetric gauge functions on 𝔄 and the unitarily invariant crossnorms on ?.- 6. A special class of symmetric gauge functions.- 7. Norm ideals and the minimal norm ideals.- 8. The uniqueness of norm for the minimal norm ideals.- 9. An open problem.

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