Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

SPECTRAL AREA ESTIMATES FOR NORMS OF COMMUTATORS

  • Cho, Muneo (DEPARTMENT OF MATHEMATICS KANAGAWA UNIVERSITY) ;
  • Nakazi, Takahiko (DEPARTMENT OF MATHEMATICS FACULTY OF SCIENCE HOKKAIDO UNIVERSITY)
  • Published : 2007.07.30
Download PDF
⟨ Previous Next ⟩

Abstract

Let A and B be commuting bounded linear operators on a Hilbert space. In this paper, we study spectral area estimates for norms of $A^*B-BA^*$ when A is subnormal or p-hyponormal.

Keywords

References

  1. H. Alexander, Projections of polynomial hulls, J. Funct. Anal. 13 (1973), 13-19 https://doi.org/10.1016/0022-1236(73)90063-3
  2. W. Arveson, Interpolation problems in nest algebras, J. Funct. Anal. 20 (1975), no. 3, 208-233 https://doi.org/10.1016/0022-1236(75)90041-5
  3. M. Cho and M. Itoh, Putnam's inequality for p-hyponormal operators, Proc. Amer. Math. Soc. 123 (1995), no. 8, 2435-2440 https://doi.org/10.2307/2161271
  4. F. Hansen, An operator inequality, Math. Ann. 246 (1979/80), no. 3, 249-250 https://doi.org/10.1007/BF01371046
  5. T. Nakazi, Complete spectral area estimates and self-commutators, Michigan Math. J. 35 (1988), no. 3, 435-441 https://doi.org/10.1307/mmj/1029003824
  6. Z. Nehari, On bounded bilinear forms, Ann. of Math. (2) 65 (1957), 153-162 https://doi.org/10.2307/1969670
  7. C. R. Putnam, An inequality for the area of hyponormal spectra, Math. Z. 116 (1970), 323-330 https://doi.org/10.1007/BF01111839
  8. D. Sarason, Generalized interpolation in $H^{\infty}$, Trans. Amer. Math. Soc. 127 (1967), 179-203 https://doi.org/10.2307/1994641
  9. B. Sz.-Nagy and C. Foias, Harmonic Analysis Of Operators On Hilbert Space, American Elsevier, New York, 1970
  10. A. Uchiyama, Berger-Shaw's theorem for p-hyponormal operators, Integral Equations Operator Theory 33 (1999), 221-230 https://doi.org/10.1007/BF01233965
  11. A. Uchiyama, Inequalities of Putnam and Berger-Shaw for p-quasihyponormal operators, Integral Equations Operator Theory 34 (1999), no. 2, 91-106 https://doi.org/10.1007/BF01332494
  12. T. Yoshino, Subnormal operators with a cyclic vector, Tohoku Math. (2) 21 (1969), 47-55 https://doi.org/10.2748/tmj/1178243033