A note on the sum of two closed lattice ideals
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- by Heinrich P. Lotz PDF
- Proc. Amer. Math. Soc. 44 (1974), 389-390 Request permission
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
- E. B. Davies, The structure and ideal theory of the predual of a Banach lattice, Trans. Amer. Math. Soc. 131 (1968), 544–555. MR 222604, DOI 10.1090/S0002-9947-1968-0222604-8
- Heinrich P. Lotz, Über das Spektrum positiver Operatoren, Math. Z. 108 (1968), 15–32 (German). MR 240648, DOI 10.1007/BF01110453
- Helmut H. Schaefer, Topological vector spaces, The Macmillan Company, New York; Collier Macmillan Ltd., London, 1966. MR 0193469
Additional Information
- © Copyright 1974 American Mathematical Society
- 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