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Halmos",,,,,Pacific,,,,Journal,,,,of,,,,Mathematics,,,,,16:,,,,421431,,,,,doi:10.2140/pjm.1966.16.421,,,,,MR0193504,,,,Enflo,,,,,Per,,,,(1976),,,,,"On,,,,the,,,,invariant,,,,subspace,,,,problem,,,,in,,,,Banach,,,,spaces",,,,,Sminaire,,,,Maurey–Schwartz,,,,(1975–1976),,,,Espaces,,,,Lp,,,,,applications,,,,radonifiantes,,,,et,,,,gomtrie,,,,des,,,,espaces,,,,de,,,,Banach,,,,,Exp.,,,,Oxford,,Journals,,Contact,,Us,,My,,Basket,,My,,Account,,.,,Halmos,,(1966),,,after,,having,,seen,,Robinson's,,preprint,,,eliminated,,the,,non-standard,,analysis,,from,,it,,and,,provided,,a,,shorter,,proof,,in,,the,,same,,issue,,of,,the,,same,,journal.,,Contents,,,,1,,,,Precise,,,,statement,,,,2,,,,History,,,,2.1,,,,Known,,,,special,,,,cases,,,,3,,,,Notes,,,,4,,,,References,,,,.,,,,The,,,vector,,,x,,,{displaystyle,,,x},,,is,,,an,,,eigenvector,,,of,,,the,,,matrix,,,A,,,{displaystyle,,,A},,,.,,,von,,,Neumann,,,showed[6],,,that,,,any,,,compact,,,operator,,,on,,,a,,,Hilbert,,,space,,,of,,,dimension,,,at,,,least,,,2,,,has,,,a,,,non-trivial,,,invariant,,,subspace.,,,(1973),,,,"Invariant,,,subspaces,,,of,,,the,,,family,,,of,,,operators,,,that,,,commute,,,with,,,a,,,completely,,,continuous,,,operator",,,,Akademija,,,Nauk,,,SSSR.,,,In,,,the,,,field,,,of,,,mathematics,,,known,,,as,,,functional,,,analysis,,,,the,,,invariant,,,subspace,,,problem,,,is,,,a,,,partially,,,unresolved,,,problem,,,asking,,,whether,,,every,,,bounded,,,operator,,,on,,,a,,,complex,,,Banach,,,space,,,sends,,,some,,,non-trivial,,,closed,,,subspace,,,to,,,itself.,,,

Argyros,,&,,Haydon,,(2009),,gave,,the,,construction,,of,,an,,infinite-dimensional,,Banach,,space,,such,,that,,every,,continuous,,operator,,is,,the,,sum,,of,,a,,compact,,operator,,and,,a,,scalar,,operator,,,so,,in,,particular,,every,,operator,,has,,an,,invariant,,subspace.,,(1985),,,,"A,,,solution,,,to,,,the,,,invariant,,,subspace,,,problem,,,on,,,the,,,space,,,l1",,,,The,,,Bulletin,,,of,,,the,,,London,,,Mathematical,,,Society,,,,17,,,(4):,,,305317,,,,doi:10.1112/blms/17.4.305,,,,MR806634,,,Read,,,,C.,,,If,,you,,require,,any,,further,,clarification,,,please,,contact,,our,,Customer,,Services,,Department.,,^,,,Page,,,401,,,in,,,Foia,,,,Ciprian;,,,Jung,,,,Il,,,Bong;,,,Ko,,,,Eungil;,,,Pearcy,,,,Carl,,,(2005).,,,Soc.,,,You,,,,can,,,,change,,,,your,,,,cookie,,,,settings,,,,at,,,,any,,,,time.,,,,References[edit].,,,,R.,,,Oxford,,Journals,,Science,,&,,Mathematics,,Journal,,London,,Mathematical,,Society,,Volume,,s2-34,,Issue,,2,,Pp.,,Nos.,,,,

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