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- W2068652604 abstract "In this paper we adopt the notion of orthogonality in Banach spaces introduced by the author in [6]. There, the author showed that in any two-dimensional subspace F of E , every nonzero element admits at most one orthogonal direction. The problem of existence of such orthogonal direction was not addressed before. Our main purpose in this paper is the investigation of this problem in the case where E is a real Banach space. As a result we obtain a characterisation of Hilbert spaces stating that, if in every two-dimensional subspace F of E every nonzero element admits an orthogonal direction, then E is isometric to a Hilbert space. We conclude by presenting some open problems." @default.
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- W2068652604 date "2005-02-01" @default.
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- W2068652604 title "A characterisation of Hilbert spaces via orthogonality and proximinality" @default.
- W2068652604 doi "https://doi.org/10.1017/s0004972700038053" @default.
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