This is an announcement for the paper "The ideal center of the dual of a Banach lattice" by Mehmet Orhon.

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.

Archive classification: math.FA

Mathematics Subject Classification: 47B38

The source file(s), center-final.tex: 25459 bytes, is(are) stored in gzipped form as 1002.4346.gz with size 8kb. The corresponding postcript file has gzipped size 84kb.

Submitted from: mo@unh.edu

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