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Weyl's theorem for p-hyponormal or M-hyponormal operators

Published online by Cambridge University Press:  25 July 2002

Atsushi Uchiyama
Affiliation:
Mathematical Institute, Tôhoku University, Sendai, 980-8578, Japan e-mail: yoshino@math.tohuku.ac.jp
Takashi Yoshino
Affiliation:
Mathematical Institute, Tôhoku University, Sendai, 980-8578, Japan e-mail: yoshino@math.tohuku.ac.jp
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In 1997, M. Cho, M. Ito and S. Oshiro showed that Weyl's theorem holds for p-hyponormal operators, for any p>0. In this note we give another proof of this result. Also, it is shown that Weyl's theorem holds for M-hyponormal operators. Further, in 1962, Stampfli showed that if T is hyponormal and its Weyl spectrum is {0} then T is compact and normal. We show that this result remains true if the hypothesis of hyponormality is replaced by either (a) p-hyponormality or (b) M-hyponormality.

Type
Research Article
Copyright
2001 Glasgow Mathematical Journal Trust