巴拿赫空间讲义（英文版）

图书标准信息

• 作者 [美]阿尔比亚克（Fernando Albiac）、Nigel J.Kalton 著
• 出版社 世界图书出版公司
• 出版时间 2012-09
• 版次 1
• ISBN 9787510048043
• 定价 59.00元
• 装帧 平装
• 开本 24开
• 纸张 胶版纸
• 页数 188页
• 正文语种 英语

【内容简介】

　　Thisbookgrewoutofaone-semestercoursegivenbythesecondauthorin2001andasubsequenttwo-semestercoursein2004-2005，bothattheUniversityofMissouri-Columbia.Thetextisintendedforagraduatestudentwhohasalreadyhadabasicintroductiontofunctionalanalysis;the'aimistogiveareasonablybriefandself-containedintroductiontoclassicalBanachspacetheory.
　　Banachspacetheoryhasadvanceddramaticallyinthelast50yearsandwebelievethatthetechniquesthathavebeendevelopedareverypowerfulandshouldbewidelydisseminatedamongstanalystsingeneralandnotrestrictedtoasmallgroupofspecialists.Thereforewehopethatthisbookwillalsoproveofinteresttoanaudiencewhomaynotwishtopursueresearchinthisareabutstillwouldliketounderstandwhatisknownaboutthestructureoftheclassicalspaces.
　　ClassicalBanachspacetheorydevelopedasanattempttoanswerverynaturalquestionsonthestructureofBanachspaces;manyofthesequestionsdatebacktotheworkofBanachandhisschoolinLvov.Itenjoyed，perhaps，itsgoldenperiodbetween1950and1980，culminatinginthedefinitivebooksbyLindenstraussandTzafriri[138]and[139]，in1977and1979respectively.Thesubjectisstillverymuchalivebutthereaderwillseethatmuchofthebasicgroundworkwasdoneinthisperiod.
　　Atthesametime，ouraimistointroducethestudenttothefundamentaltechniquesavailabletoaBanachspacetheorist.Asanexample，wespendmuchoftheearlychaptersdiscussingtheuseofSchauderbasesandbasicsequencesinthetheory.Thesimpleideaofextractingbasicsequencesinordertounderstandsubspacestructurehasbecomesecond-natureinthesubject，andsotheimportanceofthisnotionistooeasilyoverlooked.
　　Itshouldbepointedoutthatthisbookisintendedasatextforgraduatestudents，notasareferencework，andwehaveselectedmaterialwithaneyetowhatwefeelcanbeappreciatedrelativelyeasilyinaquiteleisurelytwo-semestercourse.Twoofthemostspectaculardiscoveriesinthisareaduringthelast50yearsareEnfio'ssolutionofthebasisproblem[54]andtheGowers-Maureysolutionoftheunconditionalbasicsequenceproblem[71].Thereaderwillfinddiscussionoftheseresultsbutnopresentation.Ourfeeling，basedonexperience，isthatdetouringfromthedevelopmentofthetheorytopresentlengthyandcomplicatedcounterexamplestendstobreakuptheflowofthecourse.WepreferthereforetopresentonlyrelativelysimpleandeasilyappreciatedcounterexamplessuchastheJamesspaceandTsirelson'sspace.Wealsodecided，toavoiddisruption，thatsomecounterexamplesofintermediatedifficultyshouldbepresentedonlyinthelastoptionalchapterandnotinthemainbodyofthetext.

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