%0 Journal Article
%T On the (non)existence of states on orthogonally closed subspaces in an inner product space
%A E. Chetcuti
%A P. Ptak
%J Mathematics
%D 2003
%I arXiv
%X Suppose that $S$ is an incomplete inner product space. A. Dvure\v{c}enskij shows that there are no finitely additive states on orthogonally closed subspaces, $F(S)$, of $S$ that are regular with respect to finitely dimensional spaces. In this note we show that the most important special case of the former result--the case of the evaluations given by vectors in the ``Gleason manner''--allows for a relatively simple proof. This result further reinforces the conjecture that there are no finitely additive states on $F(S)$ at all.
%U http://arxiv.org/abs/math/0301174v1