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Weyl's theorem holds for p-hyponormal operators*

  • Muneo Chō (a1), Masuo Itoh (a2) and Satoru Ōshiro (a3)

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Let ℋ be a complex Hilbert space and B(ℋ) the algebra of all bounded linear operators on ℋ. Let ℋ(ℋ) be the algebra of all compact operators of B(ℋ). For an operator T ε B(ℋ), let σ(T), σp(T), σπ(T) and πoo(T) denote the spectrum, the point spectrum, the approximate point spectrum and the set of all isolated eigenvalues of finite multiplicity of T, respectively. We denote the kernel and the range of an operator T by ker(T) and R(T), respectively. For a subset of ℋ, the norm closure of is denoted by . The Weyl spectrum ω(T) of T ε B(ℋ) is defined as the set

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Copyright

COPYRIGHT: © Glasgow Mathematical Journal Trust 1997

References

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1.Aluthge, A., On p-hyponormal operators for 0 < p < 1, Integral Equations Operator Theory 13 (1990), 307–315.
2.Baxley, J. V., Some general conditions implying Weyl's theorem, Rev. Roum. Math. Pures Appl. 16 (1971), 1163–1166.
3.Baxley, J. V., On the Weyl spectrum of a Hilbert space operator, Proc. Amer. Math. Soc. 34 (1972), 447–452.
4.Chō, M., Spectral properties of p-hyponormal operators, Glasgow Math. J. 36 (1994), 117–122.
5.Chō, M. and Huruya, T., p-hyponormal operators for 0<p<½, Comment. Math. 33 (1993), 23–29.
6.Chō, M. and Itoh, M., Putnam's Inequality for p-hyponormal operators, Proc. Amer. Math. Soc. 123 (1995), 2435–2440.
7.Chō, M. and Jin, H., On p-hyponormal operators, Nihonkai Math. J. 6 (1995), 201–206.
8.Coburn, L. A., Weyl's theorem for nonnormal operators, Michigan Math. J. 13 (1965), 285–288.
9.Patel, S. M., A note on p-hyponormal operators for 0<p<1, Integral Equations Operator Theory 21 (1965), 498–503.
10.Stampfli, J. G., Hyponormal operators, Pacific J. Math. 12 (1962), 1453–1458.
11.Xia, D., Spectral theory of hyponormal operators (Birkhäuser Verlag, Boston, 1983).
  • Cited by 8

  • Access

Weyl's theorem holds for p-hyponormal operators*

  • Muneo Chō (a1), Masuo Itoh (a2) and Satoru Ōshiro (a3)

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