Which projection, in $L_\infty$ norm or $L_2$ norm, is non-expansion?

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I am just wondering which projection is non-expansion? Basically, I am wondering if $F$ is a projection operator then which norm would satisfy the following non-expansion property, where for a given norm $\parallel \cdot \parallel$ $$\parallel FJ_1 - FJ_2\parallel \le \parallel J_1-J_2\parallel$$