Given a Banach space $E$.
Then for conjugations: $$C:E\to E:\quad C^2=1\implies\|C\|=1$$
How can I check this?
2026-04-12 21:09:32.1776028172
Conjugation: Boundedness
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Counterexample: $$ C:\mathbb{R}_2^2\to\mathbb{R}_2^2:(x,y)\mapsto(2x+y,-3x-2y) $$ Then $\Vert C((1,1))\Vert>\Vert(1,1)\Vert$