If $P_1$, $P_2$ are orthogonal projections (other than $0$) and $P_1P_2 = 0$, then show that $\left\|P_1+P_2\right\|\leq\left\|P_1\right\|+\left\|P_2\right\|$.
I hope you help me.
Orthogonal Projections: Prove that $\left\|P_1+P_2\right\|\leq\left\|P_1\right\|+\left\|P_2\right\|$
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functional-analysis
operator-theory
projective-space
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0This holds in general for linear operators, are you sure you do not mean another inequality? – 2017-02-04
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0"Norm" = "a thing where that inequality holds" (and a couple of other minor things). – 2017-02-04
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0@G.Sassatelli "minor" :) – 2017-02-04
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0@s.harp but not unimportant. – 2017-02-04