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Schauder bases and norm ideals of compact operators

Author: J. R. Holub
Journal: Proc. Amer. Math. Soc. 38 (1973), 343-348
MSC: Primary 46B15; Secondary 46L15, 46M05
MathSciNet review: 0317012
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Abstract: This paper studies the relationship between unitarily invariant crossnorms on the tensor product of Hilbert spaces and the corresponding symmetric sequence spaces. It is shown that problems concerning the behavior of norm ideals of compact operators on Hilbert space can often be treated successfully by translating the problem to one concerned with basis theory (and hence, perhaps, to one more transparent). For example, Schatten has asked for necessary and sufficient conditions that the conjugate space of a minimal norm ideal again be a minimal norm ideal. Using the ideas developed here we give such a characterization.

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Keywords: Tensor product, norm ideal, Schauder basis
Article copyright: © Copyright 1973 American Mathematical Society

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