On subspace distances determined by the Frobenius norm

Two measures of separation between two subspaces of a finite dimensional complex vector space are introduced and investigated. The measures were inspired by known expressions for the cosines of the angle and minimal angle between subspaces and are based on the Frobenius norm. By using partitioned representations of a pair of orthogonal projectors, several properties of the measures are identified and their links with other notions used to characterize a separation between subspaces are pointed out.