GTM 183巴拿赫空间理论引论（英文版）

图书标准信息

• 作者 R.E.Megginson 著
• 出版社 世界图书出版公司
• 出版时间 2003-06
• 版次 1
• ISBN 9787506259644
• 定价 58.00元
• 装帧 平装
• 开本 其他
• 纸张 胶版纸
• 页数 596页
• 正文语种 英语

【内容简介】

Sincethestudyofnormedspacesfortheirownsakeevolvedratherthanarosefullyformed，thereissomeroomtodisagreeaboutwhofoundedthefield.AlbertBennettcameclosetogivingthedefinitionofanormedspaceina1916paper[23]onanextensionofNewtonsmethodforfindingroots，andin1918FredericRiesz[195]basedageneralizationoftheFredholmtheoryofintegralequationsonthedefiningaxiomsofacompletenormedspace，thoughhedidnotusetheseaxiomstostudythegeneraltheoryofsuchspaces.AccordingtoJeanDieudonne[64]，Rieszhadatthistimeconsidereddevelopingageneraltheoryofcompletenormedspaces，butneverpublishedanythinginthisdirection.Inapaperthatappearedin1921，EduardHelly[102]provedwhatisnowcalledHellystheoremforboundedlinearfunctionals.Alongtheway，hedevelopedsomeofthegeneraltheoryofnormedspaces，butonlyinthecontextofnormsonsubspacesofthevectorspaceofallsequencesofcomplexscalars.

【目录】

Preface
1BasicConcepts
1.1Preliminaries
1.2Norms
1.3FirstPropertiesofNormedSpaces
1.4LinearOperatorsBetweenNormedSpaces
1.5BakeCategory
1.6ThreeFundamentalTheorems
1.7QuotientSpaces
1.8DirectSums
1.9TheHahn-BanachExtensionTheorems
1.10DualSpaces
1.11TheSecondDualandReflexivity
1.12Separability
1.13CharacterizationsofReflexivity
2TheWeakandWeakTopologies
2.1TopologyandNets
2.2VectorTopologies
2.3MetrizableVectorTopologies
2.4TopologiesInducedbyFamiliesofFunctions
2.5TheWeakTopology
2.6TheWeakTopology
2.7TheBoundedWeakTopology
2.8WeakCompactness
2.9JamessWeakCompactenessTheorem
2.10SupportPointsandSubreflexivity
2.11SupportPointsandSubreflexivity
3LinearOperators
3.1AdjointOperators
3.2ProjectionsandComplementedSubspaces
3.3BanachAlgebrasandSpectra
3.4CompactOperators
3.5WeaklyCompactOperators
4SchauderBases
4.1FirstPropertiesofSchauderBases
4.2UnconditionalBases
4.3EquivalentBases
4.4BasesandDuality
4.5JamessSpaceJ
5RotundityandSmoothness
5.1Rotundity
5.2UniformRotundity
5.3GeneralztionsofUniformRotundity
5.4Smoothness
5.5UnifromSmoothness
5.6GeneraliztionsofUnifromSmoothness
APrerequistes
BMetricSpaces
CTheSpaceslpanden/p，1≤p≤∞
DUltranets
References
ListofSymbols
Index