M-ideals and split faces of the quasi state space of a non-unital ordered Banach space View Full Text


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Article Info

DATE

2019-04

AUTHORS

Anindya Ghatak, Anil Kumar Karn

ABSTRACT

We characterize M-ideals in order smooth ∞-normed spaces by extending the notion of split faces of the state space to those of the quasi-state space. We also characterize approximate order unit spaces as those order smooth ∞-normed spaces V that are M-ideals in V~. Here V~ is the order unit space obtained by adjoining an order unit to V. To prove these results, we develop an order theoretic version of the “Alfsen-Efffros’ cone decomposition theorem” for order smooth 1-normed spaces. (As a quick application of this result, we sharpen a result on the extension of bounded positive linear functionals on subspaces of order smooth ∞-normed spaces). More... »

PAGES

413-429

References to SciGraph publications

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s11117-018-0614-1

DOI

http://dx.doi.org/10.1007/s11117-018-0614-1

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1107254440


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