30795.af算子空間和c代數(shù)的算子空間投射張量積

1、聲明戶(hù)巨明本學(xué)位論文是我在導(dǎo)師的指導(dǎo)下取得的研究成果，盡我所知，在本學(xué)位論文中，除了加以標(biāo)注和致謝的部分外，不包含其他人已經(jīng)發(fā)表或公布過(guò)的研究成果，也不包含我為獲得任何教育機(jī)構(gòu)的學(xué)位或?qū)W歷而使用過(guò)的材料。與我一同工作的同事對(duì)本學(xué)位論文做出的貢獻(xiàn)均已在論文中作了明確的說(shuō)明。研究生簽名：1乏壘礱埠乒勘，咿≥月妒學(xué)位論文使用授權(quán)聲明南京理工大學(xué)有權(quán)保存本學(xué)位論文的電子和紙質(zhì)文檔，可以借閱或上網(wǎng)公布本學(xué)位論文的部分或全部?jī)?nèi)容，可以向有關(guān)部門(mén)或機(jī)

2、構(gòu)送交并授權(quán)其保存、借閱或上網(wǎng)公布本學(xué)位論文的部分或全部?jī)?nèi)容。對(duì)于保密論文，按保密的有關(guān)規(guī)定和程序處理。研究生簽名：蓬彗幺么加節(jié)年≥月節(jié)曰AbstractInthispaperwefirstdefineandstudythedirectlimitofoperatorspaces，WeshowtnattheuIliquenesstheoremsforthedirectlimitofoperatorspacesunderthes喀mt坨撇e

3、otcompletelyisometricinjectionApproximatelyfinitedimensional(AF)C宰algebraswa8nroducedbyBratteliiIl【37】AsalargeclassofC木algebras，theresearchofthetheoryofAFalgebrasisveryimportantandhighlynontrivialForthis，wedefinetheappro

4、X塒眥elyfillitedilIleIlSional(AF)operatorspaces，thusAF‘a(chǎn)lgebrasbecomeaspecialcaseotAFoperatorspacesForanyAFoperatorspaceweprovethatitisagreewithadirect11mitofsomeoperatorspaces，andbesidesitsclosedsubspaceandthecorrespondin

5、gquotientsPacebothareAFoperatorSpacesTheseresultscoverthecorrespondingconclusionsin陰IfgivenAFoperatorspacesVandW，wealsoprovethattheprojectivetensorproductVp∥a11dtheinjectivetensorproductV因WofoperatorspacesarealsoAF‘opera

6、torSpaces1nadditiollTakesaki11ascleverlyconstructedanddisscussedtheinfinitetensorproductofCalgebrasin【43]，weleamhismethodandusethedirectlimitofoperatorspacestodefinethe礎(chǔ)呲eprojectivetensorproductandtheinfmiteinjectivetens

7、orproductofoperatorspacesWeextendtheembeddingtheoremofinfinitetensorproductoft木algebrasin[44]totheoperatorspacesFiIlallyweconsidertheoperatorspaceprojectivetensorpro批!毗C幸algebrasForCalgebrasVandW，weprovethattheBanach木alg

8、ebra礦0形preserves棗homomorphismandacharacterizationoftheconvergencepropertyofdualspace(y6形)willbegivenFurtherwestudytheprimeidealsofVpWandprovethatitsprimeidealsareagreewithprimitiveadealsKeywords：OperatorspaceDirectlimit，