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Addition of an identity to an ordered Banach space

  • Derek W. Robinson (a1) and Sadayuki Yamamuro (a1)

Abstract

Given an ordered Banach space ℬ equipped with an order-norm we construct a larger space ℬ¯ with an order-norm and order-identity such that B is isometrically order-isomorphic to a Banach subspace of B. We also discuss the extension of positive operators from ℬto ℬ¯.

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References

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[1]Alfsen, E. M., Compact convex sets and boundary integrals (Springer-Verlag, 1971).
[2]Arendt, W., Chernoff, P. R. and Kato, T., ‘A generalization of dissipativity and positive semigroups,’ J. Operator Theory 8 (1982), 167180.
[3]Asimov, L. and Ellis, A. J., Convexity theory and its application in functional analysis (Academic Press, 1980).
[4]Bratteli, O., Digernes, T. and Robinson, D. W., ‘Positive semigroups on ordered Banach spaces,’ J. Operator Theory, to appear.
[5]Bratteli, O. and Robinson, D. W., Operator algebras and quantum statistical mechanics, Vol. I (Springer-Verlag, 1979).
[6]Grosberg, J. and Krein, M., ‘Sur la décomposition des fonctionelles en composantes positives,’ C. R. Acad. Sci. URSS 25 (1939), 723726.
[7]Kadison, R. V., ‘A representation theory for commutative topological algebras,’ Mem. Amer. Math. Soc. No. 7 (1951).
[8]Krein, M., ‘Propriétés fondamentales des ensembles coniques normaux dans l'espace de Banach,’ C. R. Acad. Sci. URSS 28 (1940), 1317.
[9]Peressini, A. L., Ordered topological vector spaces (Harper and Rowe, 1967).
[10]Schaefer, H. H., Banach lattices and positive operators (Springer-Verlag, 1974).
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