On p-ω-hyponormal Operators.pdf

维普资讯 Chin．Quart．J．o／Math 79—84 2005，20(1)： Onp-w-hyponormalOperators YANGChang—sen，LIHai—ying (CollegeofMathematicsandInformationScience，HenanNormalUniversity，Xinxiang453002，China) Abstract：Inthispaper，weshow thatifT isp-w—hyponormM，thenonzeropointsofthe approximateandjointapproximatepointspectrumofTraeidentical；Moreover，weobtain apairofinequalitiessimilartop-w—hyponormaloperators． Keywords：Furutainequality；LSwner—Heinzinequality；approximatepointspectrum；p- 一 hyponormai operators 2000MR SubjectClassification：47B20，47A63 CLC number：0177 Documentcode：A ArticleID：1002—0462f2005)01—0079-06 §1．Introduction Inwhatfollows，H meallsacomplexHilbertspace．A boundedlinearoperatorTonH is saidtobepositive(insymbol：T 0)if(Tx，z) 0foranyz∈H．AnoperatorTissaid tobestrictlypositive(insymbol：T0、ifTispositivenadinvertible．LetTbeabounded linearoperatornadP 0．Tissaidtobep-hyponormaloperatorsif(TT)P ( )．A p-hyponormaloperatoriscalledhyponormalifP 1；semi—hyponormalifP 昙．TheL6wner— HeinzinequalityimpliesthatifT isq-hyponormal，thenitisp-hyponormalforall0P q． Callna invertibleoperatorTlog—hyponormaliflog(TT) log(TT)．LetT=UITIbethe polardecompositionofT。Aluthge9【】definedtheoperatorT=ITIUITI{whichcalledthe AluthgetrnasformationofT．AnoperatorTissaidtobeu—hyponormaliflTl ITl ITI．An operatorTissaidtobep-w—hyponormaliflTI2ITI lTlin1【0]．ClearlyofrP：1，ap-w— hyponormaloperatoris —hyponorma1．Inthispaper，wewillshowthatifTisp-w—hyponormal thenonzeropointsoftheapproximateandjointapproximatepointspectrumofTraeidentical； weobtainapairofinequalitiessimilarto3【，Theorem4】on —hyponormaloperators．Onthe Receiveddate：2003O7．O9 Foundationitem：SupportedbytheEducationFoundationofHenanProvince(2003l100O6) Biographies：YANGChang—sen(1965一)，mal