A real seminorm with square property is submultiplicative

Mohammed El Azhari (1)

1 UM5 - Université Mohammed V de Rabat [Agdal]

It was proved that every seminorm with square property on a complex associative algebra is submultiplicative. This result was obtained by using the Hirschfeld-Zelazko theorem which is not valid in the real case. Using a functional representation theorem, we show that every seminorm with square property on a real associative algebra is submultiplicative.

Mots clés: real seminorm; seminorm with square property; submultiplicative seminorm

Domaines: Analyse fonctionnelle [math.FA]

Mohammed El Azhari. A real seminorm with square property is submultiplicative. Indian Journal of Pure and Applied Mathematics, 2012, 43 (4), pp.303-307. ⟨10.1007/s13226-012-0018-z⟩. ⟨hal-01303277⟩