Lemma 1.5 . [025H]

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Lemma 1.5.

For $\phi\in\mathrm{Hom}_{k}(V,V^{\prime})$ , the set $\left\{\frac{\|\phi(v)\|^{\prime}}{\|v\|}\,\Big|\,v\in V\setminus\{0\}\right\}$ is bounded from above.