Positive Operators, Riesz Spaces, and Economics

1. Front Matter

   Pages i-vii

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2. Valuation and Optimality in Exchange Economies with a Countable Number of Agents

   • Charalambos D. Aliprantis, Donald J. Brown, Owen Burkinshaw

   Pages 1-21

3. Equilibrium Points of Non-Cooperative Random and Bayesian Games

   • Nicholas C. Yannelis, Aldo Rustichini

   Pages 23-48

4. Equilibria of Large Games with Imperfect Observability

   • Subir K. Chakrabarti, M. Ali Khan

   Pages 49-67

5. Functional Analytic Tools for Expected Utility Theory

   • Kim C. Border

   Pages 69-88

6. Remarkable Points and X _(N) -spaces

   • Yuri A. Abramovich

   Pages 89-108

7. Integration with Respect to Finitely Additive Measures

   • Wilhelmus A. J. Luxemburg

   Pages 109-150

8. Lattice-Ordered Algebras and f-Algebras: A Survey

   • Charles B. Huijsmans

   Pages 151-169

9. Approximating Derivative Securities in f-Algebras

   • Donald J. Brown, Charles B. Huijsmans, Bernardus de Pagter

   Pages 171-177

10. Some Unpleasant Objects in a Non-separable Hilbert Space

    • M. Ali Khan, Aldo Rustichini

    Pages 179-187

11. The Hopf Decomposition in Riesz Spaces

    • Radu Zaharopol

    Pages 189-194

12. Frobenius Decomposition of Positive Compact Operators

    • Ruey-Jen Jang, H. Dean Victory Jr.

    Pages 195-224

13. Irreducible Positive Operators and Hyperinvariant Ideals

    • Yuri A. Abramovich, Charalambos D. Aliprantis, Owen Burkinshaw

    Pages 225-229

Over the last fifty years advanced mathematical tools have become an integral part in the development of modern economic theory. Economists continue to invoke sophisticated mathematical techniques and ideas in order to understand complex economic and social problems. In the last ten years the theory of Riesz spaces (vector lattices) has been successfully applied to economic theory. By now it is understood relatively well that the lattice structure of Riesz spaces can be employed to capture and interpret several economic notions. On April 16-20, 1990, a small conference on Riesz Spaces, Positive Opera­ tors, and their Applications to Economics took place at the California Institute of Technology. The purpose of the conference was to bring mathematicians special­ ized in Riesz Spaces and economists specialized in General Equilibrium together to exchange ideas and advance the interdisciplinary cooperation between math­ ematicians and economists. This volume is a collection of papers that represent the talks and discussions of the participants at the week-long conference. We take this opportunity to thank all the participants of the conference, especially those whose articles are contained in this volume. We also greatly ap­ preciate the financial support provided by the California Institute of Technology. In particular, we express our sincerest thanks to David Grether, John Ledyard, and David Wales for their support. Finally, we would like to thank Susan Davis, Victoria Mason, and Marge D'Elia who handled the delicate logistics for the smooth running of the confer­ ence.

• Equilibrium
• Game Theory
• General Economic Equilibrium
• Gleichgewicht
• Hilbert space
• Spieltheorie
• agents
• ökonomisches Gleichgewicht

• Department of Mathematics, IUPUI, Indianapolis, USA

  Charalambos D. Aliprantis

• Division of Humanities and Social Sciences, California Institute of Technology, Pasadena, USA

  Kim C. Border

• Department of Mathematics, California Institute of Technology, Pasadena, USA

  Wilhelmus A. J. Luxemburg

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