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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)
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