Skip to main content

Minimal Operators from a Potential-Theoretic Viewpoint

  • Chapter
ICPT ’91

Abstract

Minimal positive operators on a Hilbert space H are characterized in terms of so-called parallel addition of operators. It is also shown how these operators can be used to reproduce the inverse, respectively generalized inverse, of any positive operator on H.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Anderson, W. N. and Duffin, R. J.: Séries and parallel addition of matrices, J. Math. Anal. Appl. 26 (1969), 576–594.

    Article  MathSciNet  MATH  Google Scholar 

  2. Anderson, W. N. and Trapp, G. E.: Shorted operators II, SIAM J. Appl. Math. 28 (1975), 60–71.

    Article  MathSciNet  MATH  Google Scholar 

  3. Ando, T.: Lebesgue-type decomposition of positive operators, Acta Sci. Math. 38 (1976), 253–260.

    MathSciNet  MATH  Google Scholar 

  4. Arsove, M. G. and Leutwiler, H.: Algebraic potential theory, Memoirs of the AMS 23, no. 226 (1980).

    Google Scholar 

  5. Arsove, M. G. and Leutwiler, H.: A unified theory of harmonie measures and capacitary potentials, Math. Z. 183 (1983), 419–442.

    Article  MathSciNet  MATH  Google Scholar 

  6. Beckenbach, E. F. and Bellman, R.: Inequalities, Ergebnisse der Math., Band 30, Springer-Verlag, Berlin—Heidelberg—New York (1965).

    Google Scholar 

  7. Brelot, M.: On Topologies and Boundaries in Potential Theory, Lecture Notes in Math., no. 175, Springer-Verlag, Berlin—Heidelberg—New York (1971).

    MATH  Google Scholar 

  8. Choquet, G.:Lectures on Analysis, vol. II, W. A. Benjamin, Inc. Reading, Massachusetts (1976).

    MATH  Google Scholar 

  9. Douglas, R. G.: On majorization, factorization, and range inclusion of operators on Hilbert space, Froc. Amer. Math. Soc. 17 (1966), 413–416.

    Article  MathSciNet  MATH  Google Scholar 

  10. Eriksson, S.-L. and Leutwiler, H.: A potential-theoretic approach to parallel addition, Math. Ann. 274 (1986), 301–317.

    Article  MathSciNet  MATH  Google Scholar 

  11. Eriksson-Bique, S.-L. and Leutwiler, H.: A generalization of parallel addition, Aeq. Math. 38 (1989), 99–110.

    Article  MathSciNet  MATH  Google Scholar 

  12. Fillmore, P. A. and Williams, J. P.: On operator ranges, Advances in Math. 7 (1971), 254–281.

    Article  MathSciNet  MATH  Google Scholar 

  13. Hirzebruch, F. and Scharlau, W.: Einführung in die Funktionalanalysis, B. I. Hochschultaschenbücher, Band 296, Bibliographisches Institut, Mannheim/Wien/Zürich (1971).

    MATH  Google Scholar 

  14. Pekarev, E. L. and Smu’jan, Ju. L.: Parallel addition and parallel subtraction of operators, Math. USSR Izv. 10 (1976), 351–370.

    Article  Google Scholar 

  15. Riesz, F. and Sz-Nagy, B.: Vorlesungen über Funktionalanalysis, VEB Deutscher Verlag der Wissenschaften, Berlin (1956).

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1994 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Eriksson-Bique, SL., Leutwiler, H. (1994). Minimal Operators from a Potential-Theoretic Viewpoint. In: Bertin, E. (eds) ICPT ’91. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-1118-8_3

Download citation

  • DOI: https://doi.org/10.1007/978-94-011-1118-8_3

  • Received:

  • Accepted:

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-4488-2

  • Online ISBN: 978-94-011-1118-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics