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- Affiliated_operator abstract "In mathematics, affiliated operators were introduced by Murray and von Neumann in the theory of von Neumann algebras as a technique for using unbounded operators to study modules generated by a single vector. Later Atiyah and Singer showed that index theorems for elliptic operators on closed manifolds with infinite fundamental group could naturally be phrased in terms of unbounded operators affiliated with the von Neumann algebra of the group. Algebraic properties of affiliated operators have proved important in L2 cohomology, an area between analysis and geometry that evolved from the study of such index theorems.".
- Affiliated_operator wikiPageID "5123403".
- Affiliated_operator wikiPageLength "5720".
- Affiliated_operator wikiPageOutDegree "37".
- Affiliated_operator wikiPageRevisionID "616733310".
- Affiliated_operator wikiPageWikiLink *-algebra.
- Affiliated_operator wikiPageWikiLink Alain_Connes.
- Affiliated_operator wikiPageWikiLink Analysis.
- Affiliated_operator wikiPageWikiLink Atiyah–Singer_index_theorem.
- Affiliated_operator wikiPageWikiLink Category:Operator_theory.
- Affiliated_operator wikiPageWikiLink Category:Von_Neumann_algebras.
- Affiliated_operator wikiPageWikiLink Centralizer_and_normalizer.
- Affiliated_operator wikiPageWikiLink Closed_manifold.
- Affiliated_operator wikiPageWikiLink Convergence_in_measure.
- Affiliated_operator wikiPageWikiLink Domain_of_a_function.
- Affiliated_operator wikiPageWikiLink Edward_Nelson.
- Affiliated_operator wikiPageWikiLink Elliptic_operator.
- Affiliated_operator wikiPageWikiLink Francis_Joseph_Murray.
- Affiliated_operator wikiPageWikiLink Fundamental_group.
- Affiliated_operator wikiPageWikiLink Gelfand–Naimark–Segal_construction.
- Affiliated_operator wikiPageWikiLink Geometry.
- Affiliated_operator wikiPageWikiLink Hilbert_space.
- Affiliated_operator wikiPageWikiLink Hilbert–Schmidt_operator.
- Affiliated_operator wikiPageWikiLink Isadore_Singer.
- Affiliated_operator wikiPageWikiLink John_von_Neumann.
- Affiliated_operator wikiPageWikiLink L²_cohomology.
- Affiliated_operator wikiPageWikiLink Mathematics.
- Affiliated_operator wikiPageWikiLink Michael_Atiyah.
- Affiliated_operator wikiPageWikiLink Partial_isometry.
- Affiliated_operator wikiPageWikiLink Polar_decomposition.
- Affiliated_operator wikiPageWikiLink Self-adjoint.
- Affiliated_operator wikiPageWikiLink Spectral_theorem.
- Affiliated_operator wikiPageWikiLink Tomita–Takesaki_theory.
- Affiliated_operator wikiPageWikiLink Unbounded_operator.
- Affiliated_operator wikiPageWikiLink Unitary_operator.
- Affiliated_operator wikiPageWikiLink Von_Neumann_algebra.
- Affiliated_operator wikiPageWikiLink Von_Neumann_regular_ring.
- Affiliated_operator wikiPageWikiLinkText "Affiliated operator".
- Affiliated_operator wikiPageWikiLinkText "affiliated operator".
- Affiliated_operator wikiPageWikiLinkText "affiliated".
- Affiliated_operator wikiPageWikiLinkText "algebra of mesurable operators".
- Affiliated_operator subject Category:Operator_theory.
- Affiliated_operator subject Category:Von_Neumann_algebras.
- Affiliated_operator type Algebra.
- Affiliated_operator type Physic.
- Affiliated_operator comment "In mathematics, affiliated operators were introduced by Murray and von Neumann in the theory of von Neumann algebras as a technique for using unbounded operators to study modules generated by a single vector. Later Atiyah and Singer showed that index theorems for elliptic operators on closed manifolds with infinite fundamental group could naturally be phrased in terms of unbounded operators affiliated with the von Neumann algebra of the group.".
- Affiliated_operator label "Affiliated operator".
- Affiliated_operator sameAs Q4688920.
- Affiliated_operator sameAs m.0d3rd8.
- Affiliated_operator sameAs Q4688920.
- Affiliated_operator wasDerivedFrom Affiliated_operator?oldid=616733310.
- Affiliated_operator isPrimaryTopicOf Affiliated_operator.