1. Let X be a Banach space and let T be a bounded linear operator on...
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1. Let X be a Banach space and let T be a bounded linear operator on X. Show that if ||T|| < 1, then I - T has a bounded inverse (I-T)-¹ on X and it holds that ∞0 1 (I – T)-¹ = ΣTN, ||(I - T) -¯`' || ≤ 1 - ||T|| | N=0 Here the series o TN converges in B(X). N=0 1. Let X be a Banach space and let T be a bounded linear operator on X. Show that if ||T|| < 1, then I - T has a bounded inverse (I-T)-¹ on X and it holds that ∞0 1 (I – T)-¹ = ΣTN, ||(I - T) -¯`' || ≤ 1 - ||T|| | N=0 Here the series o TN converges in B(X). N=0
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Related Book For
Essentials of Business Statistics
ISBN: 978-0078020537
5th edition
Authors: Bruce Bowerman, Richard Connell, Emily Murphree, Burdeane Or
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