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Positive root vectors

Published online by Cambridge University Press:  14 November 2011

Matjaž Omladič  and
Vesna Omladič
Matjaž Omladič
Affiliation:
Department of Mathematics, University of Ljubljana, Jadranska 19, 61000 Ljubljana, Slovenia
Vesna Omladič
Affiliation:
Faculty of Social Sciences, University of Ljubljana, Kardeljeva pi. 5, 61000 Ljubljana, Slovenia
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Abstract

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.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 125 , Issue 4 , 1995 , pp. 701 - 717
Copyright
Copyright © Royal Society of Edinburgh 1995

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