Convergence in trace ideals-Reference-Cited by-同舟云学术

Convergence in trace ideals

Published:1981 Issue:1 Volume:83 Page:39-43
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Simon B.

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 → A {A_n} \to A in the weak operator topology and ‖ A n ‖ → ‖ A ‖ \left \| {{A_n}} \right \| \to \left \| A \right \| , then ‖ A n − A ‖ → 0 \left \| {{A_n} - A} \right \| \to 0 .

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/1981-083-01/S0002-9939-1981-0619977-2/S0002-9939-1981-0619977-2.pdf

Reference7 articles.

1. Basic sequences, embeddings, and the uniqueness of the symmetric structure in unitary matrix spaces;Arazy, Jonathan;J. Functional Analysis,1981

2. \bysame, On the geometry of the unit ball of unitary matrix spaces, J. Integral Equations and Optim. Theory (to appear).

3. More on convergence in unitary matrix spaces;Arazy, Jonathan;Proc. Amer. Math. Soc.,1981

4. Translations of Mathematical Monographs, Vol. 18;Gohberg, I. C.,1969

5. Two theorems about 𝒞_{𝓅};Grümm, H. R.;Rep. Mathematical Phys.,1973

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