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

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