GTM 183巴拿赫空间理论引论（英文版）

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