A Banach Space Whose Elements are Classes of Sets of Constant Width
Canadian mathematical bulletin, Tome 18 (1975) no. 5, pp. 679-689

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

Let K be a compact subset of the real Euclidean space En . We say that K has constant width if the distance between each pair of distinct parallel hyperplanes which support K is constant. The collection of all compact convex subsets of En which have constant width is denoted .
Lewis, J. E. A Banach Space Whose Elements are Classes of Sets of Constant Width. Canadian mathematical bulletin, Tome 18 (1975) no. 5, pp. 679-689. doi: 10.4153/CMB-1975-119-6
@article{10_4153_CMB_1975_119_6,
     author = {Lewis, J. E.},
     title = {A {Banach} {Space} {Whose} {Elements} are {Classes} of {Sets} of {Constant} {Width}},
     journal = {Canadian mathematical bulletin},
     pages = {679--689},
     year = {1975},
     volume = {18},
     number = {5},
     doi = {10.4153/CMB-1975-119-6},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1975-119-6/}
}
TY  - JOUR
AU  - Lewis, J. E.
TI  - A Banach Space Whose Elements are Classes of Sets of Constant Width
JO  - Canadian mathematical bulletin
PY  - 1975
SP  - 679
EP  - 689
VL  - 18
IS  - 5
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1975-119-6/
DO  - 10.4153/CMB-1975-119-6
ID  - 10_4153_CMB_1975_119_6
ER  - 
%0 Journal Article
%A Lewis, J. E.
%T A Banach Space Whose Elements are Classes of Sets of Constant Width
%J Canadian mathematical bulletin
%D 1975
%P 679-689
%V 18
%N 5
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1975-119-6/
%R 10.4153/CMB-1975-119-6
%F 10_4153_CMB_1975_119_6

[1] 1. Berg, C., Shephard’s approximation theorem for convex bodies and the Milman Theorem Math. Scand. 25 (1969), 19–24. Google Scholar

[2] 2. Dunford, N. and Schwartz, J. T., Linear Operators, Part I. Interscience Publishers, Inc., New York (1957). Google Scholar

[3] 3. Eggleston, H. G., Convexity, Cambridge (1958). Google Scholar

[4] 4. Ewald, G. and Shephard, G. C., Normed vector spaces consisting of classes of convex sets. Math. Z. 91 (1966), 1–19. Google Scholar

[5] 5. Grunbaum, B., Convex Poly topes. Interscience Publishers, Inc., New York (1967). Google Scholar

[6] 6. Kelley, J. L., Namioka, I., et al., Linear Topological Spaces. D. Van Nostrand Co., Inc., Princeton (1963). Google Scholar

[7] 7. Shephard, G. C., Approximation problems for convex polyhedra. Mathematika, 11 (1964), 9–18. Google Scholar

[8] 8. Shephard, G. C., A pre-Hilbert space consisting of classes of convex subsets. Israel J. Math. 4 (1966), 1–10. Google Scholar

[9] 9. Wilanski, A., Functional analysis. Blaisdell Publ. Co., New York (1964). Google Scholar

Cité par Sources :