On the similarity of dual operators Original Research Article

Let k be a field with an involution σ and image a non-degenerate sesquilinear form, where V,W are n-dimensional k-spaces. Assume that Λset membership, variantEnd(V) and Λ*set membership, variantEnd(W) are dual operators. We show that if Λ and Λ* are similar, then Λ*=phiΛphi-1, where phi:V→W is Hermitian.