Modular functionals and perturbations of Nakano spaces

Details Modular functionals and perturbations of Nakano spaces Modular functionals and perturbations of Nakano spaces

2008-02-28

arxiv.org/abs/0802.4285v3

Journal of Logic and Analysis 1, 1 (2009) 1-42

Mathematics

Logic

Scientific paper

10.4115/jla.2009.1.1

We settle several questions regarding the model theory of Nakano spaces left open by the PhD thesis of Pedro Poitevin \cite{Poitevin:PhD}. We start by studying isometric Banach lattice embeddings of Nakano spaces, showing that in dimension two and above such embeddings have a particularly simple and rigid form. We use this to show show that in the Banach lattice language the modular functional is definable and that complete theories of atomless Nakano spaces are model complete. We also show that up to arbitrarily small perturbations of the exponent Nakano spaces are $\aleph_0$-categorical and $\aleph_0$-stable. In particular they are stable.

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