Dixmier traces of operators on Banach and Hilbert spaces |
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Authors: | Albrecht Pietsch |
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Institution: | Biberweg 7, 07749 Jena, Germany. Phone: +49 3641 946110, Fax: +49 3641 946102 |
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Abstract: | We present a simple approach to the theory of traces on the Marcinkiewicz operator ideal Particular attention is paid to the Dixmier traces, which may be obtained from both dilation‐invariant functionals and shift‐invariant functionals on $\mathfrak l_\infty$. Since the concept of positivity does not make sense for traces defined on operator ideals over Banach spaces, traces are not assumed to be positive in the Hilbert space setting, as well. This standpoint raises some new problems. The present studies will be continued in 35 , 36 . |
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Keywords: | Traces shift‐invariant functionals dilation‐invariant functionals operators MSC (2010) 47B10 46L30 |
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