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  • © 1997

Introduction to Operator Theory in Riesz Spaces

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  • ISBN: 978-3-642-60637-3
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Table of contents (22 chapters)

  1. Front Matter

    Pages I-XI
  2. Lattices and Boolean Algebras

    • Adriaan C. Zaanen
    Pages 1-11
  3. Riesz Spaces

    • Adriaan C. Zaanen
    Pages 13-26
  4. Ideals, Bands and Disjointness

    • Adriaan C. Zaanen
    Pages 27-38
  5. Archimedean Spaces and Convergence

    • Adriaan C. Zaanen
    Pages 39-53
  6. Projections and Dedekind Completeness

    • Adriaan C. Zaanen
    Pages 55-70
  7. Complex Riesz Spaces

    • Adriaan C. Zaanen
    Pages 71-81
  8. Normed Riesz Spaces and Banach Lattices

    • Adriaan C. Zaanen
    Pages 83-97
  9. Linear Operators

    • Adriaan C. Zaanen
    Pages 119-131
  10. Order Bounded Operators

    • Adriaan C. Zaanen
    Pages 133-143
  11. Order Continuous Operators

    • Adriaan C. Zaanen
    Pages 145-160
  12. Carriers of Operators

    • Adriaan C. Zaanen
    Pages 161-168
  13. Order Duals and Adjoint Operators

    • Adriaan C. Zaanen
    Pages 169-181
  14. Signed Measures and the Radon-Nikodym Theorem

    • Adriaan C. Zaanen
    Pages 183-192
  15. Embedding into the Bidual

    • Adriaan C. Zaanen
    Pages 201-208
  16. Freudenthal’s Spectral Theorem

    • Adriaan C. Zaanen
    Pages 209-219
  17. Functional Calculas and Multiplication

    • Adriaan C. Zaanen
    Pages 221-232
  18. Complex Operators

    • Adriaan C. Zaanen
    Pages 233-241

About this book

The book deals with the structure of vector lattices, i.e. Riesz spaces, and Banach lattices, as well as with operators in these spaces. The methods used are kept as simple as possible. Almost no prior knowledge of functional analysis is required. For most applications some familiarity with the oridinary Lebesgue integral is already sufficient. In this respect the book differs from other books on the subject. In most books on functional analysis (even excellent ones) Riesz spaces, Banach lattices and positive operators are mentioned only briefly, or even not at all. The present book shows how these subjects can be treated without undue extra effort. Many of the results in the book were not yet known thirty years ago; some even were not known ten years ago.

Keywords

  • Boolean algebra
  • Calc
  • Excel
  • Morphism
  • Multiplication
  • calculus
  • convergence
  • functional analysis
  • functions
  • homomorphism
  • knowledge
  • peripheral
  • spectral theorem
  • spectral theory
  • vector lattice

Authors and Affiliations

  • Delft, The Netherlands

    Adriaan C. Zaanen

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

    Adriaan C. Zaanen

Bibliographic Information

  • Book Title: Introduction to Operator Theory in Riesz Spaces

  • Authors: Adriaan C. Zaanen

  • DOI: https://doi.org/10.1007/978-3-642-60637-3

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1997

  • Softcover ISBN: 978-3-642-64487-0

  • eBook ISBN: 978-3-642-60637-3

  • Edition Number: 1

  • Number of Pages: XI, 312

  • Topics: Functional Analysis, Operator Theory

Buying options

eBook
USD 84.99
Price excludes VAT (USA)
  • ISBN: 978-3-642-60637-3
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book
USD 109.99
Price excludes VAT (USA)