Abstract
It is shown that order continuity of the norm and weak sequential completeness in non-commutative strongly symmetric spaces of τ-measurable operators are respectively equivalent to properties (u) and (V *) of Pelczynski. In addition, it is shown that each strongly symmetric space with separable (Banach) bidual is necessarily reflexive. These results are non-commutative analogues of well-known characterisations in the setting of Banach lattices.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Dodds, P.G., de Pagter, B. Properties (u) and (V*) of Pelczynski in symmetric spaces of τ-measurable operators. Positivity 15, 571–594 (2011). https://doi.org/10.1007/s11117-011-0127-7
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DOI: https://doi.org/10.1007/s11117-011-0127-7