Abstract
A normed space is a vector space F(over ℂ or ℝ), which is provided with a norm. A norm, denoted by ∥ ∥, is a real-valued functional on F, which satisfies:
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(a)
F ∋ x → ∥x∥ ≥ 0, with equality if and only if x = 0,
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(b)
∥λx∥ = |λ| ∥x∥ for every x ∈ F and λ ∈ ℂ,
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(c)
∥x + y∥ ≤ ∥x∥ + ∥y∥ for every x, y ∈ F.
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© 1998 Springer-Verlag Berlin Heidelberg
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Aubin, T. (1998). Background Material. In: Some Nonlinear Problems in Riemannian Geometry. Springer Monographs in Mathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-13006-3_3
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DOI: https://doi.org/10.1007/978-3-662-13006-3_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-08236-8
Online ISBN: 978-3-662-13006-3
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