On semicontinuous linear lattices
Author:
Hidegoro Nakano
Journal:
Proc. Amer. Math. Soc. 34 (1972), 115-117
MSC:
Primary 46A40
DOI:
https://doi.org/10.1090/S0002-9939-1972-0293370-1
MathSciNet review:
0293370
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Abstract: Applying spectral theory, we proved that a linear lattice is continuous if and only if it is semicontinuous and uniformly complete. In this paper we give another proof without use of spectral theory.
- [1] Bernard C. Anderson and Hidegoro Nakano, Semi-continuous linear lattices, Studia Math. 37 (1970/71), 191–195. MR 300049, https://doi.org/10.4064/sm-37-2-191-195
- [2] Hidegoro Nakano, Linear lattices, Wayne State University Press, Detroit, Mich., 1966. MR 0194878
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9939-1972-0293370-1
Keywords:
Functional analysis,
vector lattices
Article copyright:
© Copyright 1972
American Mathematical Society
