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Jun 22, 2021 at 10:26 comment added Matthew Daws Yes, the paper you link says that this is a "$C^*$-seminorm": I guess it's like the different between a general Banach $*$-algebra, and the very special $C^*$-norm condition $\|a^*a\| = \|a\|^2$.
Jun 22, 2021 at 9:19 comment added Math Lover Thank you Matthew. I think thats why the author in the linked paper assumes $$\|[a,a,a]\| = \| a \| ^3$$ in the definition of Ternary Banach algebra to restrict to the appropriate class of Ternary Banach Algebras?
Jun 22, 2021 at 7:46 history answered Matthew Daws CC BY-SA 4.0