Reference no: EM13990769
1. Prove that a Banach space X is reflexive if and only if its dual X 1 is reflexive. Note: "Only if" is easier.
2. Let (X, 1·1) be a normed linear space, E a closed linear subspace, and x ∈ X \E . Prove that for some f ∈ X t, f ≡ 0 on E and f (x ) = 1.
3. Show that the extension theorem for Lipschitz functions (6.1.1) does not hold for complex-valued functions. Hint: Let S = R2 with the norm 1(x, y)1 := max(|x |, |y|). Let E := {(0, 0), (0, 2), (2, 0)}, with f (0, 0) = 0, f (2, 0) = 2, and f (0, 2) = 1 + 31/2i . How to extend f to (1, 1)?
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Problem regarding the converge to an element
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Mcdonaldizing
: Simple businesses are easier to grow than technology businesses Repeatable processes make quality control easier To quickly scale geographically, one should franchise
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Complex-valued lipschitz function
: Let (S, d) be a metric space, E ⊂ S, and f a complex-valued Lipschitz function defined on E , with | f (x ) - f (y)| ≤ Kd(x, y) for all x and y in E . Show that f can be extended to all of S with | f (u) - f (v)|≤ 21/2 Kd(u, v) for all u and v in..
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A strategic plan involving five growth initiative
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Hold for complex-valued functions
: Show that the extension theorem for Lipschitz functions (6.1.1) does not hold for complex-valued functions. Hint: Let S = R2 with the norm 1(x, y)1 := max(|x |, |y|). Let E := {(0, 0), (0, 2), (2, 0)}, with f (0, 0) = 0, f (2, 0) = 2, and f (0, ..
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Entrepreneur use the growth risks assessment tool
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Continue operating the ship in the current area
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How is monasticism a utopian behavior
: How is monasticism a "Utopian" behavior, and to what degree is it also a form on counter cultural living?
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Creates quality issues or finacial stresses
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