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 |
|---|---|
| Pages (from-to) | 571-594 |
| Number of pages | 24 |
| Journal | Positivity |
| Volume | 15 |
| Issue number | 4 |
| DOIs | |
| Publication status | Published - 2011 |
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Dodds, P., & De Pagter, B. (2011). Properties (u) and (V*) of Pelczynski in symmetric spaces of T-measurable operators. Positivity, 15(4), 571-594. https://doi.org/10.1007/s11117-011-0127-7