Access the full text.
Sign up today, get DeepDyve free for 14 days.
A. Zaanen (1983)
Riesz Spaces, II
C. Aliprantis (1974)
Riesz seminorms with Fatou properties, 45
P. Meyer-Nieberg (1991)
Banach Lattices
W. Luxemburg, A. Zaanen (1963)
Notes on banach function spaces, I, 66
Z. Semadeni (1971)
Banach spaces of continuous functions
A.I. Veksler (1964)
Two problems in the theory of semiordered spaces (Russian)Sibirsk. Math. J., 5
F. Dashiell, A. Hager, M. Henriksen (1980)
Order-Cauchy Completions of Rings and Vector Lattices of Continuous FunctionsCanadian Journal of Mathematics, 32
C. Aliprantis (1974)
On the completion of Hausdorff locally solid Riesz spacesTransactions of the American Mathematical Society, 196
B.Z. Vulikh (1970)
Remarks on the completion of normed linear latticesColloq. Math., 21
I. Kawai (1957)
Locally convex lattices.Journal of The Mathematical Society of Japan, 9
H. Schaefer (1972)
On the representation of Banach lattices by continuous numerical functionsMathematische Zeitschrift, 125
C. Aliprantis, O. Burkinshaw (1978)
Locally solid Riesz spaces
B.Z. Vulikh (1953)
Some questions on the linear semiordered sets (Russian)Izvestija Akad. Nauk SSSR, Ser. Math., 17
M. Duhoux (1972)
Le complété d’un treillis localement solideBull Soc. Math. Belg., 24
H. Nakano (1953)
Linear topologies on semi-ordered linear spacesJ. Fac. Sci. Hakkaido Univ. Math., 12
D. Fremlin (1972)
On the completion of locally solid vector latticesPacific Journal of Mathematics, 43
L. Gillman, M. Jerison (1960)
Ring of Continuous Functions
W. Luxemburg (1965)
Notes on Banach Function Spaces, XIVa, 68
H. Nakano (1953)
LINEAR TOPOLOGIES ON SEMI-ORDERED LINEAR SPACESHokkaido Mathematical Journal, 12
It is known that the Banach completion Y = bX of a normed lattice X need not preserve the properties to be Dedekind complete or σ-Dedekind complete. In this paper it is proved that the countable interpolation property and the property to be sequentially order complete are preserved under the Banach completion. To prove this results we found some sufficient conditions (which are close to necessary ones) on X which secure for Y to have the countable interpolation property and (respectively) to be sequentially order complete. These conditions are obtained with the help of the newly developed techniques based on representations of normed lattices. It is well known that order continuity, and σ-order continuity of a norm are preserved under the Banach completion. Here necessary and sufficient conditions on X to secure these properties in Y are discussed.
Positivity – Springer Journals
Published: Apr 1, 2004
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.