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Traces on symmetrically normed operator ideals
-
Fedor Sukochev
and
Dmitriy Zanin
Published/Copyright:
March 23, 2012
Abstract
For every symmetrically normed ideal ℰ of compact operators, we give a criterion for the existence of a continuous singular trace on ℰ. We also give a criterion for the existence of a continuous singular trace on ℰ which respects Hardy –Littlewood majorization. We prove that the class of all continuous singular traces on ℰ is strictly wider than the class of continuous singular traces which respect Hardy –Littlewood majorization. We establish a canonical bijection between the set of all traces on ℰ and the set of all symmetric functionals on the corresponding sequence ideal. Similar results are also proved in the setting of semi-finite von Neumann algebras.
Received: 2011-03-09
Revised: 2011-08-10
Published Online: 2012-03-23
Published in Print: 2013-05
©[2013] by Walter de Gruyter Berlin Boston
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Articles in the same Issue
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- On the limit distributions of some sums of a random multiplicative function
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