## Positive linear systems: the method of positive operators |

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### Contents

Preface | 1 |

Partial orderings 3 Some Banach spaces 5 Cones and wedges 6 Passing | 12 |

Positive functionals 17 Positive operators 18 A continuity theorem 18 Exten | 24 |

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### Common terms and phrases

allows plastering approximations Banach space bounded called compact set completely regular condition cone K C E cone K+ cone of nonnegative conic interval Consequently Consider continuous functions convex set corresponding defined denote Dokl eigenvalue eigenvector equation equivalent estimate EXERCISE exists finite focussing with respect hence Hilbert space holds hypotheses of Theorem ideally convex implies inequality integral operators interior point invariant iteration procedure K+ of nonnegative kernel Krejn Lemma linear operator matrix monotone Moskva Nauk non-flatness non-zero element nonlinear nonnegative functions norm normal cone positive functional positive linear functional positive linear operator positive operators positive with respect positively invertible prove quasi-interior point reproducing cone reproducing wedge Riesz property satisfies saturated subspaces Section Show smoothness points solution spectral radius spectrum strongly minihedral subset sufficient Suppose supremum T-periodic u-bounded u-norm unit ball vector weak topology