Show that (|(g, h)|:=left(|g|^{p}+|h|^{p}ight)^{1 / p}) is for every (p geqslant 1) a norm on (mathcal{H} times
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Show that \(\|(g, h)\|:=\left(\|g\|^{p}+\|h\|^{p}ight)^{1 / p}\) is for every \(p \geqslant 1\) a norm on \(\mathcal{H} \times \mathcal{H}\). For which values of \(p\) does \(\mathcal{H} \times \mathcal{H}\) become a Hilbert space?
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Definiteness N and positive homogeneity N are obvious ...View the full answer
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