Question: 1. Let X be a Banach space and let T be a bounded linear operator on X. Show that if ||T|| < 1, then

1. Let X be a Banach space and let T be a

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)- on X and it holds that 0 1 (I T)- = TN, ||(I - T) -`' || 1 - ||T|| | N=0 Here the series o TN converges in B(X). N=0

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