On spectra ofp-hyponormal operators

The purpose of this paper is to show the following: Let 0<p<1/2. IfT=U|T| is a p-hyponormal operator with a unitaryU on a Hilbert space, then $$\sigma (T) = \mathop \cup \limits_{0 \leqslant k \leqslant 1} \sigma (T_{\left k \right]} ),$$ where $$T_{\left k \right]} = U(1 - k)S_U^ - (\left| T \right|^{2p} ) + kS_U^ + (\left| T \right|^{2p} ]^{\tfrac{1}{{2p}}} $$ andS _U ^± (T) denote the polar symbols ofT.