简介:LetB(H)bethealgebraofalltheboundedlinearoperatorsonaHilbertspaceH.ForA,PandQinB(H),ifthereexistsanoperatorX∈B(H)suchthatAPXQA=A,XQAPX=X,(QAPX)*=QAPXand(XQAP)*=XQAP,thenXissaidtobetheΓ-inverseofAassociatedwithPandQ,anddenotedbyAP,Q+.Inthisnote,wepresentsomenecessaryandsu?cientconditionsforwhichA+P,Qexists,andgiveanexplicitrepresentationofAP,Q+(ifAP,Q+exists).
简介:Thestudyofoperatorssatisfyingσja(T)=σa(T)isofsignificantinterest.Doesσja(T)=σa(T)forn-perinormaloperatorT∈B(H)ffThisquestionwasraisedbyMecheriandBraha[Oper.Matrices6(2012),725–734].Inthenoteweconstructacounterexampletothisquestionandobtainthefollowingresult:ifTisan-perinormaloperatorinB(H),thenσja(T)\{0}=σa(T)\{0}.Wealsoconsidertensorproductofn-perinormaloperators.
简介:DellaVecchiaetal.(see[2])introducedakindofmodifiedBernsteinoperatorswhichcanbeusedtoapproximatefunctionswithsingularitiesatendpointson[0,1]Inthepresentpaper,weobtainakindofpointwiseStechkin-typeinequalitiesforweightedapproximationbythemodifiedBernsetinoperators.
简介:InthispaperweproposetheqanaloguesofmodifiedBaskakov-Sz′aszoperators.Weestimatethemomentsandestablisheddirectresultsintermofmodulusofcontinuity.Anestimatefortherateofconvergenceandweightedapproximationpropertiesoftheqoperatorsarealsoobtained.
简介:为>1,让d在bidisk和一项复杂措施上表示加权的Lebesgue措施令人满意一些Carleson类型条件。在这份报纸,我们为Toeplitz操作员$T_显示出一个足够、必要的条件{\bar\mu}在加权的Bergman空间L上要跳或压缩的^\alpha$一1(d)。
简介:WeshowthatmanyharmonicanalysisoperatorsintheBesselsetting,includingmaximaloperators,Littlewood–Paley–Steintypesquarefunctions,multipliersofLaplaceorLaplace–StieltjestransformtypeandRiesztransformsare,orcanbeviewedas,Calderón–Zygmundoperatorsforallpossiblevaluesoftypeparameterλinthiscontext.Thisextendsresultsexistingintheliterature,butbeingjustifiedonlyforarestrictedrangeofλ.
简介:WestudytheboundedandthecompactweightedcompositionoperatorsfromtheBlochspaceintotheweightedBanachspacesofholomorphicfunctionsonboundedhomogeneousdomains,withparticularattentiontotheunitpolydisk.Forboundedhomogeneousdomains,wecharacterizetheboundedweightedcompositionoperatorsanddeterminetheoperatornorm.Inaddition,weprovidesufficientconditionsforcompactness.Fortheunitpolydisk,wecompletelycharacterizethecompactweightedcompositionoperators,aswellasprovide'computable'estimatesontheoperatornorm.