Let $X$ be a Banach space and $T: X\rightarrow X$, be an invertible bounded linear operator with $\|T\|=\|T^{-1}\|=1$ then can we conclude that $T$ is an isometry?
2026-03-24 22:01:23.1774389683
Bounded linear invertible operator of norm 1
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Hint: $\Vert x \Vert = \Vert T^{-1} T x \Vert \leq \Vert Tx \Vert \leq \Vert x \Vert$