Marino, Giuseppe; Pietramala, Paolamaria A note about inner products on Banach spaces. (English) Zbl 0651.46023 Boll. Unione Mat. Ital., VII. Ser., A 1, 425-427 (1987). Two vectors x and y in a Banach space X are said to be orthogonal if \(\| x\| \leq \| x+\lambda y\|\) for every real \(\lambda\). It is shown that if X is reflexive, smooth, strictly convex and of at least three dimensions, then as long as X is not Hilbert space, there exists x,y,z which are mutually orthogonal but \(x+y\) is not orthogonal to z. Reviewer: N.Ghoussoub Cited in 3 Documents MSC: 46B20 Geometry and structure of normed linear spaces 46C99 Inner product spaces and their generalizations, Hilbert spaces Keywords:inner products on Banach spaces; orthogonal vectors PDFBibTeX XMLCite \textit{G. Marino} and \textit{P. Pietramala}, Boll. Unione Mat. Ital., VII. Ser., A 1, 425--427 (1987; Zbl 0651.46023)