An algebra norm on 𝑙² whose restriction to 𝑙¹ is the usual 𝑙¹-norm

Esterle, Jean

doi:10.1090/S0002-9939-1978-0467314-9

An algebra norm on $l^{2}$ whose restriction to $l^{1}$ is the usual $l^{1}$-norm
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Proc. Amer. Math. Soc. 69 (1978), 303-307 Request permission

Abstract:

Let ${p_1}$, and ${p_2}$ be two real numbers such that ${p_2} \geqslant {p_1} \geqslant 1$. We prove that there exists an algebra norm on ${l^{{p_2}}}$ which extends the ${l^{{p_1}}}$-norm if and only if ${p_2} \leqslant 2{p_1}$.

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Automatic continuity of linear operators