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 | References | Similar Articles | Additional Information
Abstract: Suppose that is a locally convex lattice. The main results established in this note are: (a) If
are
-closed lattice ideals in the dual
of
, then
is
-closed. (b) If
is a Fréchet lattice (in particular, if
is a Banach lattice) and if
are closed lattice ideals in
, then
is closed.
- [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 0222604, https://doi.org/10.1090/S0002-9947-1968-0222604-8
- [2] Heinrich P. Lotz, Über das Spektrum positiver Operatoren, Math. Z. 108 (1968), 15–32 (German). MR 0240648, https://doi.org/10.1007/BF01110453
- [3] Helmut H. Schaefer, Topological vector spaces, The Macmillan Co., New York; Collier-Macmillan Ltd., London, 1966. MR 0193469
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9939-1974-0341020-X
Keywords:
Sum of closed lattice ideals
Article copyright:
© Copyright 1974
American Mathematical Society