Orthogonality equation almost everywhere
Jacek Chmieliński, Jürg Rätz · Publicationes Mathematicae Debrecen · 1998
For inner product spaces X and Y , we consider the orthogonality equationwhere f : X → Y and the sets M and U are, in some sense, small in X 2 and X, respectively.Under some additional assumptions we prove that for a solution f of the orthogonality equation postulated almost everywhere (in one of the two senses mentioned above) there exists a unique solution f * of the (unrestricted) orthogonality equation such that f and f * are equal almost everywhere on X.