Positive root vectors
Matjaž Omladič, Vesna Omladič · Proceedings of the Royal Society of Edinburgh Section A Mathematics · 1995
As a generalisation of the well-known result of Perron and Frobenius, it was shown by Rothblum [13] and independently by Richman and Schneider [12] that every nonzero matrix with non-negative entries has a basis of the root space corresponding to the maximal eigenvalue, represented by root vectors with non-negative entries. Krein and Rutman [9] showed that a positive compact nonquasinilpotent operator on a Banach lattice 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.