(a) Let || • || 1, || • Il2 be norms on a linear space X and let e > 0, 8 > 0 be fixed. Find conditions on the norms so that В(0, e) с В,(0, 8) holds.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.2: Norms And Distance Functions
Problem 33EQ
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(a)
Let ||· || 1 ||· ||2 be norms on a linear
space X and let ɛ > 0, 8 > 0 be fixed. Find
conditions on the norms SO that
B₁(0, ɛ) □ B₂(0, 8) holds.
Transcribed Image Text:(a) Let ||· || 1 ||· ||2 be norms on a linear space X and let ɛ > 0, 8 > 0 be fixed. Find conditions on the norms SO that B₁(0, ɛ) □ B₂(0, 8) holds.
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