Counterexample of non invertible operator
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We know the following classical statement: "Let $X$ a Banach space and $T:Xto X$ a bounded operator such that $|T|<1$ . Then $I-T$ is invertible". When we review the proof, it is easy to note how completeness of $X$ is required. But, do you know some example of a non Banach space $X$ such that there is a bounded operador $T$ with $|T|<1$ and $I-T$ is not invertible?
operator-theory operator-algebras
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asked 5 hours ago
sinbadh
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