Abstract
We present direct and self-contained proofs of the existence of singular traces on sufficiently large classes of operator ideals that live on the separable infinite-dimensional real Hilbert space. Our only tool is Banach’s version of the extension theorem of linear forms. Thanks to the use of dyadic representations of operators, all proofs have become straightforward.
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Pietsch, A. The Existence of Singular Traces on Simply Generated Operator Ideals. Integr. Equ. Oper. Theory 92, 7 (2020). https://doi.org/10.1007/s00020-019-2559-6
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DOI: https://doi.org/10.1007/s00020-019-2559-6