Glasgow Mathematical Journal



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


Atsushi  Uchiyama  a1 1 and Takashi  Yoshino  a1
a1 Mathematical Institute, Tôhoku University, Sendai, 980-8578, Japan e-mail: yoshino@math.tohuku.ac.jp

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.

(Received December 20 1999)



Footnotes

1 Research Fellow of the Japan Society for Promotion of Science.