Publications and Preprints

We define a trivolution on a complex algebra $A$ as a conjugate-linear, anti-homomorphism $\tau$ on $A$, which is its own generalized inverse, that is, $\tau^3=\tau$. We give several characterizations of trivolutions and show with examples that they appear naturally on many Banach algebras, particularly those arising from group algebras. We give several results on the existence or non-existence of involutions on the dual of a topologically introverted space. We investigate conditions under which the dual of a topologically introverted space admit trivolutions.