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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.

MSC:

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