POSITIVE ROOT VECTORS

As a generalisation of the well-known result of Perron and Frobenius, it was shown by Rothblum [13] and independently by Richman and Schneid er [12] that every nonzero matrix with non-negative entries has a basi s of the root space corresponding to the maximal eigenvalue, represent ed by root vectors with non-negative entries. Krein and Rutman [9] sho wed that a positive compact nonquasinilpotent operator on a Banach lat tice has a positive eigenvector corresponding to its spectral radius. As an extension of both results, we give sufficient conditions on such an operator in order that its spectral subspace corresponding to its spectral radius has a basis made exclusively of positive root vectors.