Geodesic
Partial Solution to Mackey's Problem about Modular Pairs and Completeness
Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 1518-1525

Voir la notice de l'article provenant de la source Cambridge University Press

Two elements A, B of a lattice are said to form a modular pair when (X ∨ A) Λ B = X ∨ (A Λ B) holds for all X ≦ B, and are said to form a dual-modular pair when (X Λ A) ∨ B = X Λ (A ∨ B) holds for all X ≧ B.We are concerned here with a particular lattice, the lattice of closed subspaces of a normed linear space, and with a question posed by Mackey in 1945 (6, p. 206, problem 2), namely:“Are there any incomplete normed linear spaces in whose lattices of closed subspaces modularity and d-modularity are equivalent?”.The principal result of this paper is the following. 
Jr., Samuel S. Holland. Partial Solution to Mackey's Problem about Modular Pairs and Completeness. Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 1518-1525. doi: 10.4153/CJM-1969-166-3
@article{10_4153_CJM_1969_166_3,
     author = {Jr., Samuel S. Holland},
     title = {Partial {Solution} to {Mackey's} {Problem} about {Modular} {Pairs} and {Completeness}},
     journal = {Canadian journal of mathematics},
     pages = {1518--1525},
     year = {1969},
     volume = {21},
     number = {1},
     doi = {10.4153/CJM-1969-166-3},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1969-166-3/}
}
TY  - JOUR
AU  - Jr., Samuel S. Holland
TI  - Partial Solution to Mackey's Problem about Modular Pairs and Completeness
JO  - Canadian journal of mathematics
PY  - 1969
SP  - 1518
EP  - 1525
VL  - 21
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1969-166-3/
DO  - 10.4153/CJM-1969-166-3
ID  - 10_4153_CJM_1969_166_3
ER  - 
%0 Journal Article
%A Jr., Samuel S. Holland
%T Partial Solution to Mackey's Problem about Modular Pairs and Completeness
%J Canadian journal of mathematics
%D 1969
%P 1518-1525
%V 21
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1969-166-3/
%R 10.4153/CJM-1969-166-3
%F 10_4153_CJM_1969_166_3

[1] 1. Amemiya, I. and Araki, H., A remark on Piron's paper, Publ. Res. Inst. Math. Sci. Ser. A 10 (1966/67), 423–427. Google Scholar

[2] 2. Banach, S., Théorie des opérations linéaires (Chelsea, New York, 1955). Google Scholar

[3] 3. Birkhoff, G., Lattice theory, 3rd éd., Amer. Math. Soc. Colloq. Publ., Vol. 25 (Amer. Math. Soc, Providence, R.I., 1967). Google Scholar

[4] 4. Goldberg, S., Unbounded linear operators: theory and applications (McGraw-Hill, New York, 1966). Google Scholar

[5] 5. Holland, S. S., Jr., On the adjoint of the product of operators, J. Functional Analysis 8 (1969), 337–344. Google Scholar

[6] 6. Mackey, G. W., On infinite-dimensional linear spaces, Trans. Amer. Math. Soc. 57 (1945), 155–207. Google Scholar

[7] 7. Schaefer, H. H., Topological vector spaces (Macmillan, New York, 1966). Google Scholar

Cité par Sources :