Positive Operators and Semigroups on Banach Lattices

1. Front Matter

   Pages i-vii

   PDF

2. Positive Operators on Krein Spaces

   • Y. A. Abramovich, C. D. Aliprantis, O. Burkinshaw

   Pages 1-22

3. A Remark on the Representation of Vector Lattices as Spaces of Continuous Real-Valued Functions

   • Yuri A. Abramovich, Wolfgang Filter

   Pages 23-26

4. Domination of Uniformly Continuous Semigroups

   • W. Arendt, J. Voigt

   Pages 27-31

5. Sums and Extensions of Vector Lattice Homomorphisms

   • S. J. Bernau

   Pages 33-45

6. Baillon’s Theorem on Maximal Regularity

   • B. Eberhardt, G. Greiner

   Pages 47-54

7. Fraction-Dense Algebras and Spaces

   • A. W. Hager, Jorge Martinez

   Pages 55-65

8. An Alternative Proof of a Radon-Nikodym Theorem for Lattice Homomorphisms

   • C. B. Huijsmans, W. A. J. Luxemburg

   Pages 67-71

9. Some Remarks on Disjointness Preserving Operators

   • C. B. Huijsmans, B. De Pagter

   Pages 73-78

10. Weakly Compact Operators and Interpolation

    • Lech Maligranda

    Pages 79-89

11. Aspects of Local Spectral Theory for Positive Operators

    • Peter Meyer-Nieberg

    Pages 91-100

12. A Wiener-Young Type Theorem for Dual Semigroups

    • Ben De Pagter

    Pages 101-109

13. Krivine’s Theorem and the Indices of a Banach Lattice

    • Anton R. Schep

    Pages 111-121

14. Representations of Archimedean Riesz Spaces by Continuous Functions

    • A. W. Wickstead

    Pages 123-133

15. Some Aspects of the Spectral Theory of Positive Operators

    • Xiao-Dong Zhang

    Pages 135-142

16. Back Matter

    Pages 143-152

    PDF

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.

• Interpolation
• Lattice
• algebra
• maximum
• semigroup
• spectral theory
• partial differential equations

• Department of Mathematics and Computer Science, Leiden University, Leiden, The Netherlands

  C. B. Huijsmans

• California Institute of Technology, Pasadena, USA

  W. A. J. Luxemburg

Policies and ethics