Skip to main content
SpringerLink
Log in

Hyponormal operators and related topics

  • Conference paper
  • First Online:
Lectures on Operator Algebras

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 247))

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 44.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 59.00
Price excludes VAT (USA)
  • Compact, lightweight 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. T. Andô, Operators with a norm condition, to appear.

    Google Scholar 

  2. T. Furuta, On the class of paranormal operators, Proc. Japan Acad. 43(1967), 594–598.

    Article  MathSciNet  MATH  Google Scholar 

  3. P. R. Halmos, Hilbert space problem book, van Nostrand, 1967.

    Google Scholar 

  4. S. Hildebrandt, Über den numerischen Wertebereich eines Operators, Math. Ann. 163 (1966), 230–247.

    Article  MathSciNet  MATH  Google Scholar 

  5. V. Istratescu, T. Saitô and T. Yoshino, On a class of operators, Tôhoku Math. J. 18 (1966), 410–413.

    Article  MATH  Google Scholar 

  6. G. H. Orland, On a class of operators, Proc. Amer. Math. Soc. 15 (1964), 75–79.

    Article  MathSciNet  MATH  Google Scholar 

  7. T. Saitô and T. Yoshino, On a conjecture of Berberian, Tôhoku Math. J. 17 (1965), 147–149.

    Article  MathSciNet  MATH  Google Scholar 

  8. T. Yoshino, On the spectrum of a hyponormal operator, Tôhoku Math. J. 17 (1965), 305–309.

    Article  MathSciNet  MATH  Google Scholar 

References

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

    Google Scholar 

  2. A. Lebow, On von Neumann's theory of spectral sets, J. Math. Anal. Appl. 7(1963), 64–90.

    Article  MathSciNet  MATH  Google Scholar 

  3. M. Schreiber, Numerical range and spectral sets, Michigan Math. J. 10(1963), 283–288.

    Article  MathSciNet  MATH  Google Scholar 

  4. B. Sz.-Nagy et C. Foias, Analyse harmonique des opérateurs de l'espace de Hilbert, Masson, Paris, 1967.

    MATH  Google Scholar 

  5. J. P. Williams, Minimal spectral sets of compact operators. Acta Sci. Math. 28(1967), 93–106.

    MathSciNet  MATH  Google Scholar 

References

  1. S. K. Berberian, Some conditions on an operator implying normality, Math. Ann. 184(1970), 188–192.

    Article  MathSciNet  MATH  Google Scholar 

  2. C. R. Putnam, Eigenvalues and boundary spectra, Illinois J. Math. 12(1968), 278–283.

    MathSciNet  MATH  Google Scholar 

  3. B. Russo, Unimodular contractions in Hilbert space, Pacific J. Math. 26(1968), 163–169.

    Article  MathSciNet  MATH  Google Scholar 

  4. T. Saitô, A theorem on boundary spectra, to appear in Acta Sci. Math.

    Google Scholar 

  5. M. Schreiber, On the spectrum of a contraction, Proc. Amer. Math. Soc. 12(1961), 709–713.

    Article  MathSciNet  MATH  Google Scholar 

  6. J. G. Stampfli, Hyponormal operators and spectral density, Trans. Amer. Math. Soc. 117(1965), 469–476.

    Article  MathSciNet  MATH  Google Scholar 

  7. B. Sz-Nagy et C. Foias, Une relation parmi les vecteurs propres d'un opérateur de l'espace de Hilbert et de l'opérateur adjoint, Acta Sci. Math. 20(1959), 91–96.

    MathSciNet  MATH  Google Scholar 

  8. T. Yoshino, On the spectrum of a hyponormal operator, Tôhoku Math. J. 17(1965), 305–309.

    Article  MathSciNet  MATH  Google Scholar 

References

  1. T. Andô, Note on invariant subspaces of a compact normal operator, Archiv der Math. 14(1963), 337–340.

    Article  MathSciNet  MATH  Google Scholar 

  2. T. Furuta, M. Horie and R. Nakamoto, A remark on a class of operators, Proc. Japan Acad. 43(1967), 607–609.

    Article  MathSciNet  MATH  Google Scholar 

  3. I. Istraţescu and G. H. Constantin, Some remarks on structure of Riesz operators, Proc. Amer. Math. Soc. 21(1969), 455–458.

    Article  MathSciNet  MATH  Google Scholar 

  4. V. Istraţescu, T. Saitô and T. Yoshino, On a class of operators, Tôhoku Math. J. 18(1966), 410–413.

    Article  MATH  Google Scholar 

  5. A. Lebow, A note on normal dilations, Proc. Amer. Math. Soc. 16(1965), 995–998.

    Article  MathSciNet  MATH  Google Scholar 

  6. C. R. Putnam, Commutation properties of Hilbert space operators and related topics, Springer-Verlag, 1967.

    Google Scholar 

  7. T. Saitô, Some remarks on Andô's theorems. Tôhoku Math. J. 18(1966), 404–409.

    Article  MathSciNet  MATH  Google Scholar 

  8. J. T. Schwartz, Subdiagonalization of operators in Hilbert space with compact imaginary part, Comm. Pure and Appl. Math. 15(1962), 159–172.

    Article  MathSciNet  MATH  Google Scholar 

  9. J. G. Stampfli, On hyponormal and Toeplitz operators, Math. Ann. 183 (1969), 328–336.

    Article  MathSciNet  MATH  Google Scholar 

  10. T. West, The decomposition of Riesz operators, Proc. London Math. Soc. 16(1966), 737–752.

    Article  MathSciNet  MATH  Google Scholar 

  11. T. Yoshino, On a problem of Bonsall, Tĥoku Math. J. 20(1968), 5–7.

    MathSciNet  MATH  Google Scholar 

References

  1. T. Andô, Operators with a norm condition, to appear.

    Google Scholar 

  2. K. H. Förster, Über Extremalpunkte des numerischen Wertebereichs eines linearen Operators, Manuscripta Math., 1(1969), 1–7.

    Article  MathSciNet  MATH  Google Scholar 

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

    Google Scholar 

  4. S. Hildebrandt, The closure of the numerical range of an operator, Commun. Pure Appl. Math. 17(1964), 415–421.

    Article  MathSciNet  MATH  Google Scholar 

  5. __________, Über den numerischen Wertebereich eines Operators, Math. Ann. 163(1966), 230–247.

    Article  MathSciNet  MATH  Google Scholar 

  6. F. Riesz and Sz.-Nagy, Functional analysis, Frederick Ungar Publication, New York, 1955.

    MATH  Google Scholar 

  7. B. Russo, Unimodular contractions in Hilbert space, Pacific J. Math. 26(1968), 163–169.

    Article  MathSciNet  MATH  Google Scholar 

  8. J. G. Stampfli, Extreme points of the numerical range of a hyponormal operator, Michigan Math. J. 13(1966), 87–89.

    Article  MathSciNet  MATH  Google Scholar 

  9. J. P. Williams, Minimal spectral sets of compact operators, Acta Sci. Math. 28(1967), 93–106.

    MathSciNet  MATH  Google Scholar 

References

  1. T. Andô, Operator with a norm condition, to appear.

    Google Scholar 

  2. A. Brown and C. Pearcy, Spectra of tensor product of operators, Proc. Amer. Math. Soc. 17(1966), 162–166.

    Article  MathSciNet  MATH  Google Scholar 

  3. T. Furata and R. Nakamoto, On tensor products of operators, Proc. Japan. Acad. 45(1969), 680–685.

    Article  MathSciNet  MATH  Google Scholar 

  4. T. Saitô, Numerical ranges of tensor products of operators. Tôhoku Math. J. 19(1967), 98–100.

    Article  MathSciNet  MATH  Google Scholar 

References

  1. C. Apostol, Sur la partie normale d'un ensemble d'opérateurs de l'espace de Hilbert, Acta Math. Acad. Sci. Hung., 17(1966) 1–4.

    Article  MathSciNet  MATH  Google Scholar 

  2. E. Durszt, On the unitary part of an operator on Hilbert space, Acta Sci. Math. 31(1970) 87–89.

    MathSciNet  MATH  Google Scholar 

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

    Google Scholar 

  4. __________ and L. J. Wallen, Powers of partial isometries, Journ. Math. and Mech. 19(1970), 657–663.

    MathSciNet  MATH  Google Scholar 

  5. B. Russo, Unimodular contractions in Hilbert space, Pacific J. Math. 26(1968), 163–169.

    Article  MathSciNet  MATH  Google Scholar 

  6. B. Sz.-Nagy et C. Foias, Analyse harmonique des opérateurs de l'espace de Hilbert, Masson, Paris, 1967.

    MATH  Google Scholar 

  7. N. Sazuki, Isometries on Hilbert spaces, Proc. Japan Acad., 39(1963), 435–438.

    Article  MathSciNet  Google Scholar 

  8. T. Yoshino, Nearly normal operators. Tôhoku Math. J. 20(1968), 1–4.

    Article  MathSciNet  MATH  Google Scholar 

References

  1. T. Andô, Operators with a norm condition, to appear.

    Google Scholar 

  2. S. K. Berberian, The numerical range of a normal operator, Duke Math. J. 31(1964), 479–483.

    Article  MathSciNet  MATH  Google Scholar 

  3. E. Durszt, Remark on a paper of S. K. Berberian, Duke Math. J. 33(1966), 795–796.

    Article  MathSciNet  MATH  Google Scholar 

  4. V. Istraţescu, On some classes of operators, Math. Ann. 188(1970), 227–232.

    Article  MathSciNet  MATH  Google Scholar 

  5. T. Saitô, A theorem of Stampfli, unpublished.

    Google Scholar 

  6. J. G. Stampfli, Hyponormal operators, Pacific J. Math. 12(1962), 1453–1458.

    Article  MathSciNet  MATH  Google Scholar 

  7. __________, Hyponormal operators and spectral density, Trans. Amer. Math. Soc. 17(1965), 469–476.

    Article  MathSciNet  MATH  Google Scholar 

  8. __________, Extreme points of the numerical range of a hyponormal operator, Michigan Math. J. 13(1966), 87–89.

    Article  MathSciNet  MATH  Google Scholar 

  9. __________, On hyponormal and Teoplitz operators, Math. Ann. 183(1969), 328–336.

    Article  MathSciNet  MATH  Google Scholar 

  10. J. P. Williams, Spectra of products and numerical range, J. Math. Anal. Appl., 17(1967), 214–220.

    Article  MathSciNet  MATH  Google Scholar 

  11. __________, Operators similar to their adjoints, Proc. Amer. Math. Soc. 20(1969), 121–123.

    Article  MathSciNet  MATH  Google Scholar 

  12. T. Yoshino, Subnormal operator with a cyclic vector Tôhoku Math. J. 21(1969), 47–55.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. College of General Education, Tohoku University, Sendai, Japan

    Teishirô Saitô

Authors
  1. Teishirô Saitô
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 1972 Springer-Verlag

About this paper

Cite this paper

Saitô, T. (1972). Hyponormal operators and related topics. In: Lectures on Operator Algebras. Lecture Notes in Mathematics, vol 247. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0058557

Download citation

  • DOI: https://doi.org/10.1007/BFb0058557

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-05729-1

  • Online ISBN: 978-3-540-37117-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation