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Proceedings of the American Mathematical Society

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A note on the sum of two closed lattice ideals


Author: Heinrich P. Lotz
Journal: Proc. Amer. Math. Soc. 44 (1974), 389-390
MSC: Primary 46A40
DOI: https://doi.org/10.1090/S0002-9939-1974-0341020-X
MathSciNet review: 0341020
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Abstract: Suppose that $ E$ is a locally convex lattice. The main results established in this note are: (a) If $ I,J$ are $ \sigma (E',E)$-closed lattice ideals in the dual $ E'$ of $ E$, then $ I + J$ is $ \sigma (E',E)$-closed. (b) If $ E$ is a Fréchet lattice (in particular, if $ E$ is a Banach lattice) and if $ I,J$ are closed lattice ideals in $ E$, then $ I + J$ is closed.


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DOI: https://doi.org/10.1090/S0002-9939-1974-0341020-X
Keywords: Sum of closed lattice ideals
Article copyright: © Copyright 1974 American Mathematical Society