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Displaying similar documents to “A formula for angles between subspaces of inner product spaces.”

Strong proximinality and polyhedral spaces.

Gilles Godefroy, V. Indumathi (2001)

Revista Matemática Complutense

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In any dual space X*, the set QP of quasi-polyhedral points is contained in the set SSD of points of strong subdifferentiability of the norm which is itself contained in the set NA of norm attaining functionals. We show that NA and SSD coincide if and only if every proximinal hyperplane of X is strongly proximinal, and that if QP and NA coincide then every finite codimensional proximinal subspace of X is strongly proximinal. Natural examples and applications are provided.

Heron's Formula and Ptolemy's Theorem

Marco Riccardi (2008)

Formalized Mathematics

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The goal of this article is to formalize some theorems that are in the [17] on the web. These are elementary theorems included in every handbook of Euclidean geometry and trigonometry: the law of cosines, the Heron's formula, the isosceles triangle theorem, the intersecting chords theorem and the Ptolemy's theorem.MML identifier: EUCLID 6, version: 7.8.09 4.97.1001

Carathéodory balls and norm balls in H p , n = z ∈ ℂ n : ∥ z ∥ p < 1

Binyamin Schwarz, Uri Srebro (1996)

Banach Center Publications

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It is shown that for n ≥ 2 and p > 2, where p is not an even integer, the only balls in the Carathéodory distance on H p , n = z ∈ ℂ n : ∥ z ∥ p < 1 which are balls with respect to the complex l p norm in ℂ n are those centered at the origin.