 Lefschetz operator of a Kähler manifold

The Lefschetz operator of a Kähler manifold is exterior multiplication by its Kähler form,Its formal adjoint is denoted by $\Lambda =L^{\ast }$ and lowers the bidegree of a differential form by $(1,1)$.

This wedge operator participates in the Kähler identities; the theorem on integral $(1,1)$ classes is a different result.