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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Measures Integrals And Martingales

ISBN: 9781316620243

2nd Edition

Authors: René L. Schilling

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Question Posted: Jan 25, 2024 01:03 AM

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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

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Definiteness N and positive homogeneity N are obvious ...View the full answer

Measures Integrals And Martingales

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