Sets invariant under projections onto two dimensional subspaces

Fitzpatrick, Simon, and Calvert, Bruce. "Sets invariant under projections onto two dimensional subspaces." Commentationes Mathematicae Universitatis Carolinae 32.2 (1991): 233-239. <http://eudml.org/doc/247287>.

@article{Fitzpatrick1991,
abstract = {The Blaschke–Kakutani result characterizes inner product spaces $E$, among normed spaces of dimension at least 3, by the property that for every 2 dimensional subspace $F$ there is a norm 1 linear projection onto $F$. In this paper, we determine which closed neighborhoods $B$ of zero in a real locally convex space $E$ of dimension at least 3 have the property that for every 2 dimensional subspace $F$ there is a continuous linear projection $P$ onto $F$ with $P(B)\subseteq B$.},
author = {Fitzpatrick, Simon, Calvert, Bruce},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {inner product space; two dimensional subspace; projection; inner product space; projection},
language = {eng},
number = {2},
pages = {233-239},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Sets invariant under projections onto two dimensional subspaces},
url = {http://eudml.org/doc/247287},
volume = {32},
year = {1991},
}

TY - JOUR
AU - Fitzpatrick, Simon
AU - Calvert, Bruce
TI - Sets invariant under projections onto two dimensional subspaces
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1991
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 32
IS - 2
SP - 233
EP - 239
AB - The Blaschke–Kakutani result characterizes inner product spaces $E$, among normed spaces of dimension at least 3, by the property that for every 2 dimensional subspace $F$ there is a norm 1 linear projection onto $F$. In this paper, we determine which closed neighborhoods $B$ of zero in a real locally convex space $E$ of dimension at least 3 have the property that for every 2 dimensional subspace $F$ there is a continuous linear projection $P$ onto $F$ with $P(B)\subseteq B$.
LA - eng
KW - inner product space; two dimensional subspace; projection; inner product space; projection
UR - http://eudml.org/doc/247287
ER -