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- Invariant_subspace_problem abstract "In the field of mathematics known as functional analysis, the invariant subspace problem for a complex Banach space H of dimension > 1 is the question whether every bounded linear operator T : H → H has a non-trivial closed T-invariant subspace (a closed linear subspace W of H which is different from {0} and H such that T(W) ⊆ W).To find a "counterexample" to the invariant subspace problem, means to answer affirmatively the following equivalent question: does there exist a bounded linear operator T : H → H such that for every non-zero vector x, the vector space generated by the sequence {T n(x) : n ≥ 0} is norm dense in H? Such operators are called cyclic.For the most important case of Hilbert spaces H the problem remains open (as of 2013), though Per Enflo found the first example of a Banach space operator with no invariant subspace.".
- Invariant_subspace_problem wikiPageExternalLink 1102994835.
- Invariant_subspace_problem wikiPageExternalLink 1102994836.
- Invariant_subspace_problem wikiPageExternalLink 0486428222.html.
- Invariant_subspace_problem wikiPageExternalLink item=GSM-50.
- Invariant_subspace_problem wikiPageID "691927".
- Invariant_subspace_problem wikiPageRevisionID "606118327".
- Invariant_subspace_problem authorlink "Charles Read".
- Invariant_subspace_problem authorlink "Per Enflo".
- Invariant_subspace_problem first "Charles".
- Invariant_subspace_problem first "Per".
- Invariant_subspace_problem hasPhotoCollection Invariant_subspace_problem.
- Invariant_subspace_problem last "Enflo".
- Invariant_subspace_problem last "Read".
- Invariant_subspace_problem year "1976".
- Invariant_subspace_problem year "1984".
- Invariant_subspace_problem year "1985".
- Invariant_subspace_problem year "1987".
- Invariant_subspace_problem year "1988".
- Invariant_subspace_problem subject Category:Functional_analysis.
- Invariant_subspace_problem subject Category:Invariant_subspaces.
- Invariant_subspace_problem subject Category:Mathematical_problems.
- Invariant_subspace_problem subject Category:Operator_theory.
- Invariant_subspace_problem subject Category:Unsolved_problems_in_mathematics.
- Invariant_subspace_problem type Abstraction100002137.
- Invariant_subspace_problem type Attribute100024264.
- Invariant_subspace_problem type Condition113920835.
- Invariant_subspace_problem type Difficulty114408086.
- Invariant_subspace_problem type InvariantSubspaces.
- Invariant_subspace_problem type MathematicalProblems.
- Invariant_subspace_problem type MathematicalSpace108001685.
- Invariant_subspace_problem type Problem114410605.
- Invariant_subspace_problem type Set107999699.
- Invariant_subspace_problem type Space100028651.
- Invariant_subspace_problem type State100024720.
- Invariant_subspace_problem type Subspace108004342.
- Invariant_subspace_problem type UnsolvedProblemsInMathematics.
- Invariant_subspace_problem comment "In the field of mathematics known as functional analysis, the invariant subspace problem for a complex Banach space H of dimension > 1 is the question whether every bounded linear operator T : H → H has a non-trivial closed T-invariant subspace (a closed linear subspace W of H which is different from {0} and H such that T(W) ⊆ W).To find a "counterexample" to the invariant subspace problem, means to answer affirmatively the following equivalent question: does there exist a bounded linear operator T : H → H such that for every non-zero vector x, the vector space generated by the sequence {T n(x) : n ≥ 0} is norm dense in H? Such operators are called cyclic.For the most important case of Hilbert spaces H the problem remains open (as of 2013), though Per Enflo found the first example of a Banach space operator with no invariant subspace.".
- Invariant_subspace_problem label "Invariant subspace problem".
- Invariant_subspace_problem label "不变子空间问题".
- Invariant_subspace_problem sameAs m.0335y4.
- Invariant_subspace_problem sameAs Q6059532.
- Invariant_subspace_problem sameAs Q6059532.
- Invariant_subspace_problem sameAs Invariant_subspace_problem.
- Invariant_subspace_problem wasDerivedFrom Invariant_subspace_problem?oldid=606118327.
- Invariant_subspace_problem isPrimaryTopicOf Invariant_subspace_problem.