Skip to main content
SpringerLink
Log in

The F. and M. Riesz theorem revisited

  • Published:
Integral Equations and Operator Theory Aims and scope Submit manuscript

Abstract

A result (Lemma 1) is obtained concerning the absolute continuity properties of operators implementing the unitary equivalence of two self-adjoint operators having a positive difference. A proof of the F. and M. Riesz theorem is given as a consequence.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

We’re sorry, something doesn't seem to be working properly.

Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

References

  1. R.G. Douglas, Banach algebra techniques in operator theory, Academic Press, 1972.

  2. P.R. Halmos, Introduction to Hilbert space and the theory of spectral multiplicity, second edition, Chelsea Pub. Co., 1951.

  3. P.R. Halmos, Shifts on Hilbert spaces, Jour. reine angew. Math., 208 (1961), 102–112.

    Google Scholar 

  4. P.R. Halmos, A glimpse into Hilbert space, Lectures on modern mathematics, vol. 1, Wiley, 1963, 1–22.

    Google Scholar 

  5. P.R. Halmos, A Hilbert space problem book, van Nostrand Co., 1967.

  6. K. Hoffman, Banach spaces of analytic functions, Prentice-Hall, 1962.

  7. E. Hopf, Ergodentheorie, Ergebnisse der Math., 5, Chelsea Pub. Co., 1948.

  8. C.R. Putnam, On differences of unitarily equivalent self-adjoint operators, Proc. Glas. Math. Assoc., 4 (1960), 103–107.

    Google Scholar 

  9. C.R. Putnam, Commutators, perturbations, and unitary spectra, Acta Math., 106 (1961), 215–232.

    Google Scholar 

  10. C.R. Putnam, Commutation properties of Hilbert space operators and related topics, Ergebnisse der Math., 36, Springer, 1967.

  11. F. Riesz and M. Riesz, Über die Randwerte einer analytischen Funktion, Quat. Cong. des Math. Scand. Stockholm (1916), 27–44.

    Google Scholar 

  12. W. Rudin, Real and complex analysis, McGraw-Hill Book Co., 1966.

  13. D.E. Sarason, The theorem of F. and M. Riesz on the absolute continuity of analytic measures, unpublished note circulated c. 1963.

  14. D.E. Sarason, Invariant subspaces, Topics in operator theory, Edit. C. Pearcy, Math. Surveys, No. 13, Amer. Math. Soc., 1974, 1–47.

  15. J. Wermer, On invariant subspaces of normal operators, Proc. Amer. Math. Soc., 3 (1952), 270–277.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Purdue University, 47907, West Lafayette, IN, USA

    C. R. Putnam

Authors
  1. C. R. Putnam
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

This work was supported by a National Science Foundation research grant.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Putnam, C.R. The F. and M. Riesz theorem revisited. Integr equ oper theory 3, 508–514 (1980). https://doi.org/10.1007/BF01702313

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01702313

Keywords

Search

Navigation