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Is $A \mapsto \|A\|_{op}^2$ a smooth function? Specifically, is the space of matrices equipped with operator norm a 2-smooth Banach space?

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    $\begingroup$ Let $A_t=\text{diag}(1+t,1-t)$. Then $\|A_t\|=1+|t|$. $\endgroup$
    – Anthony Quas
    Commented Oct 24, 2019 at 20:26

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