In this paper, we construct infinitely many bi-invariantmetrics on the Hamiltonian diffeomorphism group and study their basic properties and corresponding generalizations of the Hofer inequality and Sikorav one.
"A CLASS OF NEW BI-INVARIANT METRICS ON THE HAMILTONIAN DIFFEOMORPHISM GROUPS." Taiwanese J. Math. 19 (4) 1111 - 1143, 2015. https://doi.org/10.11650/tjm.19.2015.5098