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.
Original language | English |
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Pages (from-to) | 571-594 |
Number of pages | 24 |
Journal | Positivity |
Volume | 15 |
Issue number | 4 |
DOIs | |
Publication status | Published - 2011 |