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arXiv · 1002.4346

The ideal center of the dual of a Banach lattice

Mehmet Orhon
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Abstract

Let $E$ be a Banach lattice. Its ideal center $Z(E)$ is embedded naturally in the ideal center $Z(E')$ of its dual. The embedding may be extended to a contractive algebra and lattice homomorphism of $Z(E)"$ into $Z(E')$. We show that the extension is onto $Z(E')$ if and only if $E$ has a topologically full center. (That is, for each $x\in E$, the closure of $Z(E)x$ is the closed ideal generated by $x$.) The result can be generalized to the ideal center of the order dual of an Archimedean Riesz space and in a modified form to the orthomorphisms on the order dual of an Archimedean Riesz space.

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Mehmet Orhon. 2010-02-23. The ideal center of the dual of a Banach lattice. https://arxiv.org/abs/1002.4346

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