A note on triadjoints of biorthomorphisms

Abstract

Let $X$ be a vector lattice and a bilinear mapping $T : X \times X \to X$ be a biorthomorphism. The triadjoint of $T$ is a biorthomorphism and the space of all biorthomorphisms on bidual of $X$ is an $f$-algebra. If $X = A$ is an $f$-algebra, then the set of all orthomorphisms on the order bidual of $A$ is an order ideal of the set of all biorthomorphisms on order bidual of $A$. In particular case, it is a band of it.