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15 صفحه اولAllometry constants of finite-dimensional spaces: theory and computations
We describe the computations of some intrinsic constants associated to an n-dimensional normed space V, namely the N -th “allometry” constants κ∞(V) := inf { ‖T‖ · ‖T ′‖, T : `∞ → V, T ′ : V → `∞, TT ′ = IdV } . These are related to Banach–Mazur distances and to several types of projection constants. We also present the results of our computations for some low-dimensional spaces such as sequenc...
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Example 3. If X ⊆ RN is a vector space then it is a vector subspace of RN . Example 4. R1 is a vector subspace of R2. But the set [−1, 1] is not a vector subspace because it is not closed under either vector addition or scalar multiplication (for example, 1 + 1 = 2 6∈ [−1, 1]). Geometrically, a vector space in RN looks like a line, plane, or higher dimensional analog thereof, through the origin...
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ژورنال
عنوان ژورنال: Mathematische Nachrichten
سال: 2017
ISSN: 0025-584X
DOI: 10.1002/mana.201600448