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About: Invariant subspace problem     Goto   Sponge   NotDistinct   Permalink

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Type: yago:WikicatMathematicalProblemsyago:WikicatUnsolvedProblemsInMathematicsyago:Abstraction100002137yago:Attribute100024264yago:Condition113920835yago:Difficulty114408086yago:MathematicalSpace108001685yago:Problem114410605yago:WikicatInvariantSubspacesyago:Set107999699yago:Space100028651yago:State100024720yago:Subspace108004342 New Facet based on Instances of this Class

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. Many variants of the problem have been solved, by restricting the class of bounded operators considered or by specifying a particular class of Banach spaces. The problem is still open for separable Hilbert spaces (in other words, each example, found so far, of an operator with no non-trivial invariant subspaces is an operator that acts on a Banach space that is not isomorphic to a separable Hilbert space).