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Birkhäuser

Positivity and its Applications

Positivity X, 8-12 July 2019, Pretoria, South Africa

  • Conference proceedings
  • © 2021

Overview

Editors:
  1. Eder Kikianty

    1. Department of Mathematics, University of Pretoria, Hatfield, South Africa

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  2. Mokhwetha Mabula

    1. Department of Mathematics, University of Pretoria, Hatfield, South Africa

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  3. Miek Messerschmidt

    1. Department of Mathematics, University of Pretoria, Hatfield, South Africa

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  4. Jan Harm van der Walt

    1. Department of Mathematics, University of Pretoria, Hatfield, South Africa

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  5. Marten Wortel

    1. Department of Mathematics, University of Pretoria, Hatfield, South Africa

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  • Features selected contributions from the conference Positivity X
  • Deals with ordered mathematical structures and their applications
  • Covers a broad spectrum of topics

Part of the book series: Trends in Mathematics (TM)

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Table of contents (16 papers)

  1. Front Matter

    Pages i-x
    Download chapter PDF

  2. Coenraad Christoffel Andries Labuschagne

    • J. J. Grobler
    Pages 1-3

  3. Inverse Monotonicity of Elliptic Operators in Variational Form

    • Roumen Anguelov, Nduduzo Majozi
    Pages 5-19

  4. On Compact Operators Between Lattice Normed Spaces

    • Youssef Azouzi, Mohamed Amine Ben Amor
    Pages 21-29

  5. How to Be Positive in Natural Sciences?

    • Jacek Banasiak
    Pages 31-62

  6. Real Positive Maps and Conditional Expectations on Operator Algebras

    • David P. Blecher
    Pages 63-102

  7. Free Vector Lattices and Free Vector Lattice Algebras

    • Marcel de Jeu
    Pages 103-139

  8. On Disjointness, Bands and Projections in Partially Ordered Vector Spaces

    • Jochen Glück
    Pages 141-171

  9. 101 Years of Vector Lattice Theory: A Vector Lattice-Valued Daniell Integral

    • Jacobus J. Grobler
    Pages 173-192

  10. Ergodicity in Riesz Spaces

    • Jonathan Homann, Wen-Chi Kuo, Bruce A. Watson
    Pages 193-201

  11. Multiplicative Representation of Real-Valued bi-Riesz Homomorphisms on Partially Ordered Vector Spaces

    • Anke Kalauch, Onno van Gaans
    Pages 203-215

  12. Orthogonality: An Antidote to Kadison’s Anti-Lattice Theorem

    • Anil Kumar Karn
    Pages 217-227

  13. Binary Relations in Mathematical Economics: On Continuity, Additivity and Monotonicity Postulates in Eilenberg, Villegas and DeGroot

    • M. Ali Khan, Metin Uyanik
    Pages 229-250

  14. On Fixed Point Theory in Partially Ordered (Quasi-)metric Spaces and an Application to Complexity Analysis of Algorithms

    • M. D. Mabula, J. J. Miñana, O. Valero
    Pages 251-266

  15. Inheritance Properties of Positive Cones Induced by Subalgebras and Quotients of Ordered Banach Algebras

    • Kelvin Muzundu
    Pages 267-273

  16. Universally Complete Spaces of Continuous Functions

    • Jan Harm van der Walt
    Pages 275-281

  17. Applications of Generalized B∗-Algebras to Quantum Mechanics

    • Martin Weigt
    Pages 283-318

  18. Back Matter

    Pages 319-321
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Keywords

About this book

This proceedings volume features selected contributions from the conference Positivity X. The field of positivity deals with ordered mathematical structures and their applications. At the biannual series of Positivity conferences, the latest developments in this diverse field are presented. The 2019 edition was no different, with lectures covering a broad spectrum of topics, including vector and Banach lattices and operators on such spaces, abstract stochastic processes in an ordered setting, the theory and applications of positive semi-groups to partial differential equations, Hilbert geometries, positivity in Banach algebras and, in particular, operator algebras, as well as applications to mathematical economics and financial mathematics. The contributions in this book reflect the variety of topics discussed at the conference. They will be of interest to researchers in functional analysis, operator theory, measure and integration theory, operator algebras, and economics.

Positivity X was dedicated to the memory of our late colleague and friend, Coenraad Labuschagne. His untimely death in 2018 came as an enormous shock to the Positivity community. He was a prominent figure in the Positivity community and was at the forefront of the recent development of abstract stochastic processes in a vector lattice context.


Editors and Affiliations

  • Department of Mathematics, University of Pretoria, Hatfield, South Africa

    Eder Kikianty, Mokhwetha Mabula, Miek Messerschmidt, Jan Harm van der Walt, Marten Wortel

Bibliographic Information

  • Book Title: Positivity and its Applications

  • Book Subtitle: Positivity X, 8-12 July 2019, Pretoria, South Africa

  • Editors: Eder Kikianty, Mokhwetha Mabula, Miek Messerschmidt, Jan Harm van der Walt, Marten Wortel

  • Series Title: Trends in Mathematics

  • DOI: https://doi.org/10.1007/978-3-030-70974-7

  • Publisher: Birkhäuser Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer Nature Switzerland AG 2021

  • Hardcover ISBN: 978-3-030-70973-0Published: 23 July 2021

  • Softcover ISBN: 978-3-030-70976-1Published: 24 July 2022

  • eBook ISBN: 978-3-030-70974-7Published: 22 July 2021

  • Series ISSN: 2297-0215

  • Series E-ISSN: 2297-024X

  • Edition Number: 1

  • Number of Pages: X, 321

  • Number of Illustrations: 2 b/w illustrations, 2 illustrations in colour

  • Topics: Functional Analysis, Operator Theory, Measure and Integration, Applications of Mathematics

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