hw8 - ≤ k v k 2 ≤ C 2 k v k 1 for all v ∈ V(Hint To...

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HW # 8 Due date: 4/5/2011 page 125: 27,28,30 page 158: 1,2,8,9 1. Suppose that < - , - > 1 and < - , - > 2 are two distinct inner products on a vector space V and that k•k 1 and k•k 2 are their corresponding norms. Show that there exists constants C 1 and C 1 such that C 1 k v k 1
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Unformatted text preview: ≤ k v k 2 ≤ C 2 k v k 1 for all v ∈ V . (Hint: To prove the leftmost inequality, write v with respect to a basis of V which is orthonormal with respect to < • , • > 2 .) Exam 2 is on April 14th. 1...
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