Sets invariant under projections onto one dimensional subspaces
Fitzpatrick, Simon ; Calvert, Bruce
Commentationes Mathematicae Universitatis Carolinae, Tome 32 (1991), p. 227-232 / Harvested from Czech Digital Mathematics Library
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The Hahn--Banach theorem implies that if $m$ is a one dimensional subspace of a t.v.s. $E$, and $B$ is a circled convex body in $E$, there is a continuous linear projection $P$ onto $m$ with $P(B)\subseteq B$. We determine the sets $B$ which have the property of being invariant under projections onto lines through $0$ subject to a weak boundedness type requirement.

Publié le : 1991-01-01
Classification:  46A55,  52A07,  52A10 
@article{116960,
     author = {Simon Fitzpatrick and Bruce Calvert},
     title = {Sets invariant under projections onto one  dimensional subspaces},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {32},
     year = {1991},
     pages = {227-232},
     zbl = {0756.52002},
     mrnumber = {1137783},
     language = {en},
     url = {http://dml.mathdoc.fr/item/116960}
}

Fitzpatrick, Simon; Calvert, Bruce. Sets invariant under projections onto one  dimensional subspaces. Commentationes Mathematicae Universitatis Carolinae, Tome 32 (1991) pp. 227-232. http://gdmltest.u-ga.fr/item/116960/

Schaeffer H.H. Topological Vector Spaces, MacMillan, N.Y., 1966. | MR 0193469