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Spectral properties of p-hyponormal operators

  • Muneo Chō (a1)

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Let ℋ be a complex Hilbert space and B(ℋ) be the algebra of all bounded linear opeators on ℋ. An operator T ∈ B() is said to be p-hyponormal if (T*T)p–(TT*)p. If p = 1, T is hyponormal and if p = ½ is semi-hyponormal. It is well known that a p-hyponormal operator is p-hyponormal for qp. Hyponormal operators have been studied by many authors. The semi-hyponormal operator was first introduced by D. Xia in [7]. The p-hyponormal operators have been studied by A. Aluthge in [1]. Let T be a p-hyponormal operator and T=U|T| be a polar decomposition of T. If U is unitary, Aluthge in [1] proved the following properties.

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References

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1.Aluthge, A., On p-Hyponormal operators for 0< p<1, Integral Equations and Operator Theory 13 (1990), 307315.
2.Chō, M. and Takaguchi, M., Some classes of commuting n-tuples of operators, Studia Math. 80 (1984), 246259.
3.Curto, R., On the Connectedness of Invertible n-tuples, Indiana Univ. Math. J. 29 (1980), 393406.
4.Furuta, T., On the polar decomposition of an operator, Acta Sci. Math. (Szeged) 46 (1983), 261268.
5.Putnam, C. R., Spectra of polar factors of hyponormal operators, Trans. Amer. Math. Soc. 188 (1974), 419428.
6.Taylor, J. L., A joint spectrum for several commuting operators, J. Functional Analysis 6 (1970), 172191.
7.Xia, D., On the nonnormal operators-semihyponormal operators, Sci. Sinica 23 (1983), 700713.
8.Xia, D., Spectral theory of hyponormal operators (Birkhäuser Verlag, Basel, 1983).
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Glasgow Mathematical Journal
  • ISSN: 0017-0895
  • EISSN: 1469-509X
  • URL: /core/journals/glasgow-mathematical-journal
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