On the Theory of Lp(Lq)-Banach Lattices
On the Theory of Lp(Lq)-Banach Lattices
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Lp(Lq)-Banach格子理论
DOI：
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发表时间：
2007
期刊：
影响因子：
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通讯作者：
Y. Raynaud
中科院分区：
文献类型：
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作者：
Ward Henson;Y. Raynaud
设1≤ p，q < ∞，设BLpLq是所有Banach格X的类，使得X等距格同构于某个Lp（Lq）-Banach格中的一个带.我们证明了BLpLq-Banach格上正压缩投影的值域是BLpLq中的正压缩投影。这是这个定理和以前的结果的一个后果，BLpLq是一阶可公理化的语言的Banach格。通过研究任意BLpLq-Banach格被有限维子格所覆盖的问题，我们给出了BLpLq的一组显式公理。我们还考虑了Lp（Lq）-Banach格的所有子格的类;对于这个类（当p/q不是整数时），我们给出了一组公理，这些公理类似于Krivine关于Lp-Banach空间的子空间（当p/2不是整数时）的著名公理。我们还将这个结果推广到极限情形q = ∞。
Given 1≤ p,q < ∞, let BLpLq be the class of all Banach lattices X such that X is isometrically lattice isomorphic to a band in some Lp(Lq)-Banach lattice. We show that the range of a positive contractive projection on any BLpLq-Banach lattice is itself in BLpLq. It is a consequence of this theorem and previous results that BLpLq is first-order axiomatizable in the language of Banach lattices. By studying the pavings of arbitrary BLpLq-Banach lattices by finite dimensional sublattices that are themselves in this class, we give an explicit set of axioms for BLpLq. We also consider the class of all sublattices of Lp(Lq)-Banach lattices; for this class (when p/q is not an integer) we give a set of axioms that are similar to Krivine’s well-known axioms for the subspaces of Lp-Banach spaces (when p/2 is not an integer). We also extend this result to the limiting case q = ∞.