Preservers of pairs of bivectors with bounded distance

We extend Liu’s fundamental theorem of the geometry of alternate matrices to the second exterior power of an infinite dimensional vector space and also use her theorem to characterize surjective mappings T from the vector space V of all n×n alternate matrices over a field with at least three elements onto itself such that for any pair A, B in V, rank(A-B)⩽2k if and only if rank(T(A)-T(B))⩽2k, where k is a fixed positive integer such that n⩾2k+2 and k⩾2.