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- Weyl–von_Neumann_theorem abstract "In mathematics, the Weyl–von Neumann theorem is a result in operator theory due to Hermann Weyl and John von Neumann. It states that, after the addition of a compact operator (Weyl (1909)) or Hilbert–Schmidt operator (von Neumann (1935)) of arbitrarily small norm, a bounded self-adjoint operator or unitary operator on a Hilbert space is conjugate by a unitary operator to a diagonal operator. The results are subsumed in later generalizations for bounded normal operators due to David Berg (1971, compact perturbation) and Dan-Virgil Voiculescu (1979, Hilbert–Schmidt perturbation). The theorem and its generalizations were one of the starting points of operator K-homology, developed first by Larry Brown, Ronald Douglas and Peter Fillmore and, in greater generality, by Gennadi Kasparov.In 1958 Kuroda showed that the Weyl–von Neumann theorem is also true if the Hilbert–Schmidt class is replaced by any Schatten class Sp with p ≠ 1. For S1, the trace-class operators, the situation is quite different. The Kato–Rosenblum theorem, proved in 1957 using scattering theory, states that if two bounded self-adjoint operators differ by a trace-class operator, then their absolutely continuous parts are unitarily equivalent. In particular if a self-adjoint operator has absolutely continuous spectrum, no perturbation of it by a trace-class operator can be unitarily equivalent to a diagonal operator.".
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- Weyl–von_Neumann_theorem wikiPageWikiLink Category:K-theory.
- Weyl–von_Neumann_theorem wikiPageWikiLink Category:Operator_theory.
- Weyl–von_Neumann_theorem wikiPageWikiLink Category:Theorems_in_functional_analysis.
- Weyl–von_Neumann_theorem wikiPageWikiLink Compact_operator.
- Weyl–von_Neumann_theorem wikiPageWikiLink Dan-Virgil_Voiculescu.
- Weyl–von_Neumann_theorem wikiPageWikiLink Decomposition_of_spectrum_(functional_analysis).
- Weyl–von_Neumann_theorem wikiPageWikiLink Graduate_Studies_in_Mathematics.
- Weyl–von_Neumann_theorem wikiPageWikiLink Hermann_Weyl.
- Weyl–von_Neumann_theorem wikiPageWikiLink Hilbert_space.
- Weyl–von_Neumann_theorem wikiPageWikiLink Hilbert–Schmidt_operator.
- Weyl–von_Neumann_theorem wikiPageWikiLink John_von_Neumann.
- Weyl–von_Neumann_theorem wikiPageWikiLink K-homology.
- Weyl–von_Neumann_theorem wikiPageWikiLink Mathematics.
- Weyl–von_Neumann_theorem wikiPageWikiLink Normal_operator.
- Weyl–von_Neumann_theorem wikiPageWikiLink Operator_theory.
- Weyl–von_Neumann_theorem wikiPageWikiLink Ronald_Douglas.
- Weyl–von_Neumann_theorem wikiPageWikiLink Ronald_G._Douglas.
- Weyl–von_Neumann_theorem wikiPageWikiLink Scattering_theory.
- Weyl–von_Neumann_theorem wikiPageWikiLink Schatten_class_operator.
- Weyl–von_Neumann_theorem wikiPageWikiLink Self-adjoint_operator.
- Weyl–von_Neumann_theorem wikiPageWikiLink Trace-class_operator.
- Weyl–von_Neumann_theorem wikiPageWikiLink Trace_class.
- Weyl–von_Neumann_theorem wikiPageWikiLink Unitary_operator.
- Weyl–von_Neumann_theorem wikiPageWikiLinkText "Weyl–von Neumann theorem".
- Weyl–von_Neumann_theorem hasPhotoCollection Weyl–von_Neumann_theorem.
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- Weyl–von_Neumann_theorem wikiPageUsesTemplate Template:Harvtxt.
- Weyl–von_Neumann_theorem wikiPageUsesTemplate Template:Mathanalysis-stub.
- Weyl–von_Neumann_theorem subject Category:K-theory.
- Weyl–von_Neumann_theorem subject Category:Operator_theory.
- Weyl–von_Neumann_theorem subject Category:Theorems_in_functional_analysis.
- Weyl–von_Neumann_theorem comment "In mathematics, the Weyl–von Neumann theorem is a result in operator theory due to Hermann Weyl and John von Neumann. It states that, after the addition of a compact operator (Weyl (1909)) or Hilbert–Schmidt operator (von Neumann (1935)) of arbitrarily small norm, a bounded self-adjoint operator or unitary operator on a Hilbert space is conjugate by a unitary operator to a diagonal operator.".
- Weyl–von_Neumann_theorem label "Weyl–von Neumann theorem".
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- Weyl–von_Neumann_theorem sameAs Q7990342.
- Weyl–von_Neumann_theorem sameAs Q7990342.
- Weyl–von_Neumann_theorem wasDerivedFrom Weyl–von_Neumann_theorem?oldid=675192577.
- Weyl–von_Neumann_theorem isPrimaryTopicOf Weyl–von_Neumann_theorem.