Abstract
In section 14 we shall show that when μ is a finite measure L p (T, Σ, μ,ℂ) can be faithfully represented as a Banach lattice in terms of countable direct sums of spaces L p ([0,1]m, ℂ) where m is an infinite cardinal number and [0,1]m is m products of [0,1] with product Lebesgue measure being considered. We also discuss the isomorphic classification of these spaces.
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© 1974 Springer-Verlag Berlin · Heidelberg
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Lacey, H.E. (1974). Representation Theorems for Spaces of the Type L p (T,Σ,μ,ℂ). 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_5
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DOI: https://doi.org/10.1007/978-3-642-65762-7_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-65764-1
Online ISBN: 978-3-642-65762-7
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