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- Symmetrizable_compact_operator abstract "In mathematics, a symmetrizable compact operator is a compact operator on a Hilbert space that can be composed with a positive operator with trivial kernel to produce a self-adjoint operator. Such operators arose naturally in the work on integral operators of Hilbert, Korn, Lichtenstein and Marty required to solve elliptic boundary value problems on bounded domains in Euclidean space. Between the late 1940s and early 1960s the techniques, previously developed as part of classical potential theory, were abstracted within operator theory by various mathematicians, including M. G. Krein, William T. Reid, Peter Lax and Jean Dieudonné. Fredholm theory already implies that any element of the spectrum is an eigenvalue. The main results assert that the spectral theory of these operators is similar to that of compact self-adjoint operators: any spectral value is real; they form a sequence tending to zero; any generalized eigenvector is an eigenvector; and the eigenvectors span a dense subspace of the Hilbert space.".
- Symmetrizable_compact_operator wikiPageID "36719170".
- Symmetrizable_compact_operator wikiPageLength "8776".
- Symmetrizable_compact_operator wikiPageOutDegree "26".
- Symmetrizable_compact_operator wikiPageRevisionID "619074060".
- Symmetrizable_compact_operator wikiPageWikiLink Category:Operator_theory.
- Symmetrizable_compact_operator wikiPageWikiLink Category:Potential_theory.
- Symmetrizable_compact_operator wikiPageWikiLink Compact_operator.
- Symmetrizable_compact_operator wikiPageWikiLink Eigenvalues_and_eigenvectors.
- Symmetrizable_compact_operator wikiPageWikiLink Elliptic_boundary_value_problem.
- Symmetrizable_compact_operator wikiPageWikiLink Euclidean_space.
- Symmetrizable_compact_operator wikiPageWikiLink Fredholm_determinant.
- Symmetrizable_compact_operator wikiPageWikiLink Fredholm_operator.
- Symmetrizable_compact_operator wikiPageWikiLink Generalized_eigenvector.
- Symmetrizable_compact_operator wikiPageWikiLink Hilbert_space.
- Symmetrizable_compact_operator wikiPageWikiLink Hilbert–Schmidt_operator.
- Symmetrizable_compact_operator wikiPageWikiLink Jean_Dieudonné.
- Symmetrizable_compact_operator wikiPageWikiLink Mark_Krein.
- Symmetrizable_compact_operator wikiPageWikiLink Mathematics.
- Symmetrizable_compact_operator wikiPageWikiLink Operator_theory.
- Symmetrizable_compact_operator wikiPageWikiLink Peter_Lax.
- Symmetrizable_compact_operator wikiPageWikiLink Positive_element.
- Symmetrizable_compact_operator wikiPageWikiLink Potential_theory.
- Symmetrizable_compact_operator wikiPageWikiLink Schatten_class_operator.
- Symmetrizable_compact_operator wikiPageWikiLink Spectral_theory.
- Symmetrizable_compact_operator wikiPageWikiLink Spectrum.
- Symmetrizable_compact_operator wikiPageWikiLink Trace_class.
- Symmetrizable_compact_operator wikiPageWikiLinkText "symmetrizable compact operator".
- Symmetrizable_compact_operator wikiPageUsesTemplate Template:Citation.
- Symmetrizable_compact_operator wikiPageUsesTemplate Template:Harvtxt.
- Symmetrizable_compact_operator wikiPageUsesTemplate Template:Reflist.
- Symmetrizable_compact_operator subject Category:Operator_theory.
- Symmetrizable_compact_operator subject Category:Potential_theory.
- Symmetrizable_compact_operator hypernym Operator.
- Symmetrizable_compact_operator type Company.
- Symmetrizable_compact_operator type Function.
- Symmetrizable_compact_operator type Physic.
- Symmetrizable_compact_operator comment "In mathematics, a symmetrizable compact operator is a compact operator on a Hilbert space that can be composed with a positive operator with trivial kernel to produce a self-adjoint operator. Such operators arose naturally in the work on integral operators of Hilbert, Korn, Lichtenstein and Marty required to solve elliptic boundary value problems on bounded domains in Euclidean space.".
- Symmetrizable_compact_operator label "Symmetrizable compact operator".
- Symmetrizable_compact_operator sameAs Q7661324.
- Symmetrizable_compact_operator sameAs m.0l8d5c_.
- Symmetrizable_compact_operator sameAs Q7661324.
- Symmetrizable_compact_operator wasDerivedFrom Symmetrizable_compact_operator?oldid=619074060.
- Symmetrizable_compact_operator isPrimaryTopicOf Symmetrizable_compact_operator.