Properties (u) and (V*) of Pelczynski in symmetric spaces of T-measurable operators

Peter Dodds; Bernardus De Pagter

doi:10.1007/s11117-011-0127-7

Properties (u) and (V*) of Pelczynski in symmetric spaces of T-measurable operators

Peter Dodds, Bernardus De Pagter

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

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	https://doi.org/10.1007/s11117-011-0127-7
Publication status	Published - 2011

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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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AU - De Pagter, Bernardus

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AB - 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.

U2 - 10.1007/s11117-011-0127-7

DO - 10.1007/s11117-011-0127-7

M3 - Article

VL - 15

SP - 571

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JO - Positivity

JF - Positivity

SN - 1385-1292

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ER -