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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Convergence in trace ideals


Author: B. Simon
Journal: Proc. Amer. Math. Soc. 83 (1981), 39-43
MSC: Primary 47D25; Secondary 47B10
DOI: https://doi.org/10.1090/S0002-9939-1981-0619977-2
MathSciNet review: 619977
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Abstract: We give an elementary proof of a theorem of Arazy which presents necessary and sufficient conditions on a symmetric sequence so that the associated symmetrically normed trace ideal has the property that if $ {A_n} \to A$ in the weak operator topology and $ \left\Vert {{A_n}} \right\Vert \to \left\Vert A \right\Vert$, then $ \left\Vert {{A_n} - A} \right\Vert \to 0$.


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DOI: https://doi.org/10.1090/S0002-9939-1981-0619977-2
Article copyright: © Copyright 1981 American Mathematical Society