Linear approximation of approximately biorthogonality preserving maps (Q2644025)

The author has studied linear properties of mappings from a bounded domain of an \(n\)-dimensional normed space into another \(n\)-dimensional normed space such that the image of some almost biorthogonal system is almost biorthogonal. Thus, a generalization of the author's result on stability of orthogonality in Euclidean spaces is obtained. The results are quite interesting and their proofs are given in a simple and elegant manner. The reader is referred to the following volume for further results in the subject: \textit{T. M. Rassias} (ed.), Inner product spaces and applications. Pitman Res. Notes Math. Ser. 376. Harlow: Longman (1997; Zbl 0882.00018).