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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

An algebra norm on $ l\sp{2}$ whose restriction to $ l\sp{1}$ is the usual $ l\sp{1}$-norm


Author: Jean Esterle
Journal: Proc. Amer. Math. Soc. 69 (1978), 303-307
MSC: Primary 46H05
DOI: https://doi.org/10.1090/S0002-9939-1978-0467314-9
MathSciNet review: 0467314
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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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DOI: https://doi.org/10.1090/S0002-9939-1978-0467314-9
Article copyright: © Copyright 1978 American Mathematical Society