• Published : 2005.08.01


In this paper it is proved that quasisimilar n-tuples of tensor products of injective p-quasihyponormal operators have the same spectra, essential spectra and indices, respectively. And it is also proved that a Weyl n-tuple of tensor products of injective p-quasihyponormal operators can be perturbed by an n-tuple of compact operators to an invertible n-tuple.


  1. A. Aluthge, On p-hyponormal operators for 0 < p < 1, Integral Equations Operator Theory 13 (1990), 307-315
  2. L. Chen, Y. Zikun, and R. Yingbin, Common properties of operators RS and SR and p-hyponormal operators, Integral Equations Operator Theory 43 (1999), 313-325
  3. R. E. Curto, Applications of several complex variables to multiparameter spectral theory, Surveys of some recent results in operator theory, J. B. Conway and B. B. Morrel, eds., vol. II, Pitman Res. Notes in Math. Ser. 192, Longman Publ. Co., London, 1988, 25-90
  4. R. E. Curto, Problems in multivariable operator theory, Contemp. Math. 120, Amer. Math. Soc. Providence, RI, 1991
  5. B. P. Duggal, p-Hyponormal operators satisfy Bishop's condition ($\beta$), Integral Equations Operator Theory 40 (2001), 436-440
  6. B. P. Duggal, Tensor products of operators-strong stability and p-hyponormality, Glasg. Math. J. 42 (2000), 371-381
  7. B. P. Duggal and I. H. Jeon, On n-tuples of tensor products of p-hyponormal operators, J. Korea Soc. Math. Educ. Ser. B Pure Appl. Math. 11 (2004), 287-292
  8. P. Duggal and I. H. Jeon, On p-quasihyponormal operators, preprint, 2004
  9. J. Eschmeier and M. Putinar, Spectral decompositions and analytic sheaves, Oxford University Press, Oxford, 1996
  10. C. Foias, I. B. Jung, E. Ko, and C. Pearcy, Complete contractivity of maps associated with the Aluthge and Duggal transforms, Pacific J. Math. 209 (2003), 249-259
  11. R. Gelca, Compact perturbations of Fredholm n-tuples, Proc. Amer. Math. Soc. 122 (1994), 195-198
  12. I. H. Jeon and B. P. Duggal, p-Hyponormal operators and quasisimilarity, Integral Equations Operator Theory 49 (2004), 397-403
  13. I. H. Jeon, J. I. Lee, and A. Uchiyama, On p-quasihyponormal operators and quasisimilarity, Math. Inequal. Appl. 6 (2003), 309-315
  14. I. H. Kim, Tensor products of quasihyponormal operators, Math. Inequal. Appl., to appear
  15. M. Putinar, On Weyl spectrum in several variables, Math. Japonica 50 (1999), 355-357
  16. M. Putinar, Quasi-similarity of tuples with Bishop's property ($\beta$), Integral Equations Operator Theory 15 (1992), 1047-1052
  17. J. Snader, Bishop's condition ($\beta$), Glasg. Math. J. 26 (1985), 35-46
  18. K. Tanahashi and Uchiyama, Isolated point of spectrum of p-qusihyponormal operators, Linear Algebra Appl. 341 (2002), 345-350
  19. J. L. Taylor, The analytic functional mathcalculus for several commuting operators, Acta Math. 125 (1970), 1-38
  20. A. Uchiyama, Inequalities of Putnam and Berger-Shaw for p-quasihyponormal operators, Integral Equations Operator Theory 34 (1999), 91-106
  21. R.Wolff, Bishop's property ($\beta$) for tensor product tuples of operators, J. Operator Theory 42 (1999), 371-377
  22. R. Yingbin and Y. Zikun, Spectral structure and subdecomposability of p-hyponormal operators, Proc. Amer. Math. Soc. 128 (1999), 2069-2074