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Orthogonal constant mappings in isosceles orthogonal spaces. (English) Zbl 1144.46305
Given a so-called isosceles orthogonal space $$X$$ and a normed space $$Y$$, the authors call a map $$c:X\to Y$$ orthogonally constant if $$c(x+y)=c(x-y)$$ for all $$x,y\in X$$ with $$x\perp y$$. Afterwards they prove some stability results of such maps w.r.t. small perturbations.

##### MSC:
 46C50 Generalizations of inner products (semi-inner products, partial inner products, etc.) 47B37 Linear operators on special spaces (weighted shifts, operators on sequence spaces, etc.) 47B32 Linear operators in reproducing-kernel Hilbert spaces (including de Branges, de Branges-Rovnyak, and other structured spaces)