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• W2892492657 abstract "We characterize M-ideals in order smooth $$infty $$-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 $$infty $$-normed spaces V that are M-ideals in $$tilde{V}$$. Here $$tilde{V}$$ 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 $$infty $$-normed spaces)." @default.
• W2892492657 created "2018-10-05" @default.
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• W2892492657 creator A5055439801 @default.
• W2892492657 date "2018-09-26" @default.
• W2892492657 modified "2023-10-16" @default.
• W2892492657 title "M-ideals and split faces of the quasi state space of a non-unital ordered Banach space" @default.
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• W2892492657 doi "https://doi.org/10.1007/s11117-018-0614-1" @default.
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