p-亚正常算子的本质谱与拟相似

Essential Spectrum of p-Hyponormal Operators and Quasisimilarity

本文证明了每一个ｐ－亚正常算子Ａ，都相应存在一个亚正常算子 ，使得Ａ与 有相同的闭值域点、相同的本质谱和谱．由此推出如果Ａ是ｐ－亚正常算子，Ｂ是任一有界线性算子，若存在有界线性算子Ｘ有稠值域，使得ＸＢ＝ＡＸ，则σ（Ａ）（Ｂ）此外还证明了，如果Ａ是ｐ－亚正常算子且 Ｒ（Ａ）闭或ＫｅｒＡ＝ＫｅｒＡ*， Ｂ是任一有界线性算子，Ａ与Ｂ拟相似，则ｅ（Ａ）（Ｂ）．

In this paper, we prove that for every p-hyponormal operator A, there corresponds a hyponormal operator A such that A and A have the same closed range points and same essential spectrum and same spectrum. This is then used to derive that if A is a p - hyponormal operator, B is any bounded linear operator and there exists a dense range operator X such that XB = AX, then (A) (B). We also prove that if A is a p-hyponormal operator and R(A) is closed or KerA = KerA , B is any bounded linear operator, B and A are quasisimilar, then (A) (B).