Sets invariant under projections onto one dimensional subspaces

Fitzpatrick, Simon, and Calvert, Bruce. "Sets invariant under projections onto one dimensional subspaces." Commentationes Mathematicae Universitatis Carolinae 32.2 (1991): 227-232. <http://eudml.org/doc/247251>.

@article{Fitzpatrick1991,
abstract = {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.},
author = {Fitzpatrick, Simon, Calvert, Bruce},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {convex; projection; Hahn–Banach; subsets of $\mathbb \{R\}^2$; convexity; projections; Hahn-Banach theorem; subsets of },
language = {eng},
number = {2},
pages = {227-232},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Sets invariant under projections onto one dimensional subspaces},
url = {http://eudml.org/doc/247251},
volume = {32},
year = {1991},
}

TY - JOUR
AU - Fitzpatrick, Simon
AU - Calvert, Bruce
TI - Sets invariant under projections onto one dimensional subspaces
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1991
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 32
IS - 2
SP - 227
EP - 232
AB - 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.
LA - eng
KW - convex; projection; Hahn–Banach; subsets of $\mathbb {R}^2$; convexity; projections; Hahn-Banach theorem; subsets of
UR - http://eudml.org/doc/247251
ER -