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During the last twenty-five years, the development of the theory of Banach lattices has stimulated new directions of research in the theory of positive operators and the theory of semigroups of positive operators. In particular, the recent investigations in the structure of the lattice ordered (Banach) algebra of the order bounded operators of a Banach lattice have led to many important results in the spectral theory of positive operators. The contributions contained in this volume were presented as lectures at a conference organized by the Caribbean Mathematics Foundation, and provide an overview of the present state of development of various areas of the theory of positive operators and their spectral properties.
This book will be of interest to analysts whose work involves positive matrices and positive operators.
Positive Operators on Krein Spaces.- A Remark on the Representation of Vector Lattices as Spaces of Continuous Real-Valued Functions.- Domination of Uniformly Continuous Semigroups.- Sums and Extensions of Vector Lattice Homomorphisms.- Baillon’s Theorem on Maximal Regularity.- Fraction-Dense Algebras and Spaces.- An Alternative Proof of a Radon—Nikodym Theorem for Lattice Homomorphisms.- Some Remarks on Disjointness Preserving Operators.- Weakly Compact Operators and Interpolation.- Aspects of Local Spectral Theory for Positive Operators.- A Wiener—Young Type Theorem for Dual Semigroups.- Krivine’s Theorem and Indices of a Banach Lattice.- Representations of Archimedean Riesz Spaces by Continuous Functions.- Some Aspects of the Spectral Theory of Positive Operators.- Problem Section.