P-弱亚正规算子的Riesz幂等元和Weyl定理

On the Riesz Idempotent Element and Weyl's Theorem of P-w-hyponormal Operators

主要研究了P-弱亚正规算子T的Riesz幂等元Ek和T的Aluthge变换T的Riesz幂等元Eh的性质，其中λ=isoσ（T）．证明了EλH=EλH，得到了当λ≠0时，Eλ是自伴算子，Eλ=Eλ和EλH=ker（T—λ）=ker（T—λ），而且证出了Weyl定理对T及f（r），f∈H（σ（T））都适合．

This paper mainly researches into the characteristics of the Riesz idempotent element Eλ of P -w -hyponormal operator T and the Riesz idempotent element Eλ of the Aluthge transformation of T, in which λ = isoσ（T）. It is proved that EλH = EλH, and when λ≠0, Eλ is the self- adjoint operator, Eλ =Eλ and EλH =ker（T- λ） =ker（T - λ） . And it is also proved that Weyl＇ s Theorem is suitable for both T and f （T）, and f∈ n（σ（T））.