Positive approximate identities and lattice-ordered dual spaces |
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Authors: | Bertram Walsh |
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Institution: | 1. Department of Mathematics, Rutgers University, 08903, New Brunswick, New Jersey, USA
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Abstract: | It is shown that if E7] is a locally convex space ordered by a closed, generating positive cone K satisfying certain mild hypotheses relating K and 7, then E′ is lattice-ordered by the dual cone K′ whenever the identity linear transformation on E is the pointwise limit of sums of transformations x→〈x,x′〉z where z∈K and x′∈K′. The converse is true for certain classes of spaces, e.g., Fréchet spaces. |
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