On the Gram-Schmidt projection in normed spaces. (English) Zbl 0819.46010

Summary: We consider various kinds of orthogonal projections in normed spaces, and in particular the so-called Gram-Schmidt projection, which can be explicitly found. By this projection, we characterize in several ways the existence of inner product, give a procedure for the left \(g\)- orthogonalization of a sequence of vectors, and prove several geometric facts. For instance, we prove that the theorem on three normals is valid in some normed spaces.


46B20 Geometry and structure of normed linear spaces
46C99 Inner product spaces and their generalizations, Hilbert spaces