Let X be a normed lattice and Y be the norm completion of X with a natural embedding π : X → Y . By the Kawai- Luxemburg theorem, X is embedded as an order dense set and π preserves all suprema and infima iff X satisfies the condition (A o ) (i.e., the norm has pseudo σ-Lebesgue property). Let X o be the largest ideal in X having the condition (A o ); let Y (o) be the band in Y generated by π X o and Y (1) be the complementary band to Y (o) . The structure of Y and, in particular, of the bands Y (o) and Y (1) are studied. The conditions for Y (o) to be a projection band and π X o to be topologically dense in Y (o) are obtained.
Positivity – Springer Journals
Published: Oct 13, 2006
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