Integral Equations and Operator Theory

, Volume 13, Issue 3, pp 307–315 | Cite as

Onp-hyponormal operators for 0<p<1

  • Ariyadasa Aluthge


The distance formula ‖Tt-λI)−1‖=[Dist(λ, σ(T)]−1, λ∉σ(T), for hyponormal operators, is generalized top-hyponormal operators for 0<p<1. Several other results involving eigenspaces ofU and |T|, the joint point spectrum, and the spectral radius are also otained, where |T|=(T*T)1/2 andU is the unitary operator in the polar decomposition of thep-hyponormal operatorT=U|T|.


Unitary Operator Spectral Radius Point Spectrum Polar Decomposition Joint Point 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    K. F. Clancey, Seminormal Operators, Lecture notes in Math. No. 742, 1980.Google Scholar
  2. [2]
    R. G. Donoghue, Montone Matrix Functions and Analytic Continuation, Springer-Verlag, 1974.Google Scholar
  3. [3]
    T. Furuta,A≥B≥0 assures(B r Ap Br)1/q≥B(p+2r)/q andA p(+2r)/q≥(Ar Bp Ar)1/q forr≥0,a≥1 with (1+2r)q≥p+2r, Proc. Amer. Math. Soc.101(1987), 85–88.Google Scholar
  4. [4]
    K. Löwner, Uber monotone matrix functione, Math. Z.38(1934), 177–216.Google Scholar
  5. [5]
    G. K. Pederson and M. Takesaki, The operator equationTHT=K, Proc. Amer. Math. Soc.36(1972), 311–312.Google Scholar
  6. [6]
    C. R. Putnam, Commutation Properties of Hilbert space operators, Eng. Math. Greng. No. 36, Berling 1967.Google Scholar
  7. [7]
    J. G. Stampfli, Hyponormal operators, Pacific Journal of Math.12(1962), 1453–1458.Google Scholar
  8. [8]
    J. G. Stampfli, Hyponormal operators and spectral density, Tran. Amer. Math. Soc.117(1965), 469–476.Google Scholar
  9. [9]
    D. Xia, On the nonnormal operators-semihyponormal operators, Sci. Sinica23(1980), 700–713.Google Scholar
  10. [10]
    D. Xia, Spectral Theory of Hyponormal Operators, Birkhäuser Verlag, Boston, 1983.Google Scholar

Copyright information

© Birkhäuser Verlag 1990

Authors and Affiliations

  • Ariyadasa Aluthge
    • 1
  1. 1.Department of MathematicsVanderbilt UniversityNashvilleUSA

Personalised recommendations