Abstract
In section 16 we prove that the only real Banach lattices which have the property that every closed sublattice is the range of a positive contractive projection are the lattices L p (μ, ℝ) and c0(Г, ℝ) for some measure μ and some index set Г. We also prove a similar joint characterization of abstract M and L p spaces in terms of simultaneous linear extensions.
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© 1974 Springer-Verlag Berlin · Heidelberg
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Lacey, H.E. (1974). Characterizations of Abstract M and L p Spaces. In: The Isometric Theory of Classical Banach Spaces. Die Grundlehren der mathematischen Wissenschaften, vol 208. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-65762-7_6
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DOI: https://doi.org/10.1007/978-3-642-65762-7_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-65764-1
Online ISBN: 978-3-642-65762-7
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