Sets of uniformly absolutely continuous norm in symmetric spaces of measurable operators

Dodds, P.; de Pagter, B.; Sukochev, F.

doi:10.1090/tran/6477

Sets of uniformly absolutely continuous norm in symmetric spaces of measurable operators
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by P. G. Dodds, B. de Pagter and F. Sukochev PDF

Trans. Amer. Math. Soc. 368 (2016), 4315-4355 Request permission

Abstract:

We characterise sets of uniformly absolutely continuous norm in strongly symmetric spaces of $\tau$-measurable operators. Applications are given to the study of relatively weakly compact and relatively compact sets and to compactness properties of operators dominated in the sense of complete positivity by compact or by Dunford-Pettis operators.

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