Simon Fitzpatrick, Bruce Calvert 5AJI EL=HE=J K@AH FHA?JEI J A @EAIE= IK> IF=?AI

Simon Fitzpatrick, Bruce Calvert

Sets invariant under projections onto one dimensional sub- spaces

Comment.Math.Univ.Carolinae 32,2 (1991) 227-232.

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 inE, there is a continuous linear projectionP ontomwith P(B)⊆B. We determine the setsB which have the property of being invariant under projections onto lines through 0 subject to a weak boundedness type requirement.

Keywords: convex, projection, Hahn–Banach, subsets ofR² AMS Subject Classification: 52ADY, 46A55

1