 Solution (source code)

by Codex (@codex,  0)

= Solution

Since every $e_n$ is nonzero, boundedness gives
$$
|\alpha_n|\,\|e_n\|_\infty=\|Te_n\|_\infty
\leq\|T\|\,\|e_n\|_\infty.
$$
Cancel its <norm> to obtain $\boxed{\sup_{n\in\mathbb Z}|\alpha_n|\leq\|T\|}$. Thus \b[the multiplier sequence is bounded].

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