Skip to main content

Constructive Unbounded Operators

  • Chapter
  • 296 Accesses

Part of the book series: Synthese Library ((SYLI,volume 306))

Abstract

The existence of points outside the domain of an unbounded linear map‑ ping between normed spaces is investigated constructively.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Michael Beeson, Foundations of Constructive Mathematics, Springer-Verlag, Heidelberg, 1985.

    MATH  Google Scholar 

  2. Errett Bishop, Foundations of Constructive Analysis, McGraw-Hill, New York, 1967.

    Google Scholar 

  3. Errett Bishop and Douglas Bridges, Constructive Analysis, Grundlehren math. Wiss. 279, Springer-Verlag, Heidelberg, 1985.

    Google Scholar 

  4. Douglas Bridges, Computability: A Mathematical Sketchbook, Graduate Texts in Mathematics 146, Springer-Verlag, Heidelberg, 1994.

    Google Scholar 

  5. Douglas Bridges, “Constructive mathematics and unbounded operators a reply to Hellman”, J. Philos. Logic 24, 549–561, 1995.

    Article  MathSciNet  MATH  Google Scholar 

  6. Douglas Bridges and Hajime Ishihara, “Linear mappings are fairly well—behaved”, Arch. Math. 54, 558–562, 1990.

    Article  MathSciNet  MATH  Google Scholar 

  7. Douglas Bridges, William Julian, and Ray Mines, “A constructive treatment of open and unopen mapping theorems”, Zeit. math. Logik und Grundlagen der Math. 35, 29–43, 1989.

    Article  MathSciNet  MATH  Google Scholar 

  8. Douglas Bridges and Fred Richman, Varieties of Constructive Mathematics,London Math. Soc. Lecture Notes 97, Cambridge University Press, 1987.

    Google Scholar 

  9. Douglas Bridges, Fred Richman, and Peter Schuster, “Adjoints, absolute values, and polar decompositions”, J. Operator Theory 44, 243–254, 2000.

    MathSciNet  MATH  Google Scholar 

  10. Geoffrey Hellman, “Constructive mathematics and quantum mechanics: unbounded operators and the spectral theorem”, J. Phil. Logic 22, 221–248, 1993.

    Article  MathSciNet  MATH  Google Scholar 

  11. ] Hajime Ishihara, “Continuity and nondiscontinuity in constructive mathematics”, J. Symbolic Logic 56 (4), 1349–1354, 1991.

    Article  MathSciNet  MATH  Google Scholar 

  12. Hajime Ishihara, “A constructive proof of Banach’s inverse mapping theorem”, New Zealand J. Math. 23 (1), 71–75, 1994.

    MathSciNet  MATH  Google Scholar 

  13. R.V. Kadison and J.R. Ringrose, Fundamentals of the Theory of Operator Algebras ( 2 Vols), Academic Press, New York, 1983.

    MATH  Google Scholar 

  14. Fred Richman, “Intuitionism as generalization”, Philosophia Math. 5, 124–128, 1990.

    MathSciNet  MATH  Google Scholar 

  15. Fred Richman, “Interview with a constructive mathematician”, Modern Logic 6, 247–271, 1996.

    MathSciNet  MATH  Google Scholar 

  16. Halsey L. Royden, “Aspects of constructive analysis”, in Errett Bishop: Reflections on Him and His Research, Contemporary Mathematics 39, Amer. Math. Soc., Providence RI, 1985.

    Google Scholar 

  17. Walter Rudin, Functional Analysis ( 2nd edn ), McGraw-Hill, New York, 1991.

    MATH  Google Scholar 

  18. A.S. Troelstra and D. van Dalen, Constructivism in Mathematics: An Introduction (two volumes). North—Holland, Amsterdam, 1988.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2001 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Bridges, D., Ishihara, H. (2001). Constructive Unbounded Operators. In: Schuster, P., Berger, U., Osswald, H. (eds) Reuniting the Antipodes — Constructive and Nonstandard Views of the Continuum. Synthese Library, vol 306. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9757-9_3

Download citation

  • DOI: https://doi.org/10.1007/978-94-015-9757-9_3

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-5885-0

  • Online ISBN: 978-94-015-9757-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics