On Urbanik's Axioms for Absolute Valued Algebras with Involution

Abstract

We prove that, in Urbanik's (Urbanik 1961) definition of absolute valued algebras with involution, the axiom ‖ a*‖ = ‖ a‖ (the unique one which relates the absolute value ‖·‖ and the involution *) is redundant.

Key Words:

• Absolute-valued algebra
• Involution

2000 Mathematics Subject Classification:

• Primary 46E15, 46B04
• Secondary 46H70

ACKNOWLEDGMENT

Partially supported by Junta de Andalucía grants FQM 0199 and FQM 1215, and Project I+D MCYT MTM-2004-03882.

Notes

Communicated by A. Elduque.