Self adjoint operators on a Hilbert space – math.stackexchange.com

Self adjoint operators on a Hilbert space – math.stackexchange.com

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Let $H$ be a Hilbert space and let $T\in \mathcal{B}(H)$ such that $T$ is self-adjoint. I want to show that if $T$ is non-zero, then $T^n\neq 0$ for all $n\in \mathbb{N}$. Suppose $n$ be the least ...

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