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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
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.

References [Enhancements On Off] (What's this?)

  • [1] E. B. Davies, The structure and ideal theory of the predual of a Banach lattice, Trans. Amer. Math. Soc. 131 (1968), 544-555. MR 36 #5654. MR 0222604 (36:5654)
  • [2] H. P. Lotz, Über das Spektrum positiver Operatoren, Math. Z. 108 (1968), 15-32. MR 39 #1994. MR 0240648 (39:1994)
  • [3] H. H. Schaefer, Topological vector spaces, Macmillan, New York, 1966. MR 33 #1689. MR 0193469 (33:1689)

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Keywords: Sum of closed lattice ideals
Article copyright: © Copyright 1974 American Mathematical Society

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