About: Symmetrizable compact operator

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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

Attributes	Values
rdf:type	company
rdfs:label	Symmetrizable compact operator (en)
rdfs: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. 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 (en)
dcterms:subject	Operator theory Potential theory
Wikipage page ID	36719170 (xsd:integer)
Wikipage revision ID	1117757215 (xsd:integer)
Link from a Wikipage to another Wikipage	Trace-class operator Peter Lax Operator theory Potential theory Mathematics Elliptic boundary value problem Operator theory Eigenvalue Eigenvector Fredholm determinant Generalized eigenvector Compact operator Spectral theory Spectrum Euclidean space Hilbert–Schmidt operator Positive operator Hilbert space Jean Dieudonné Potential theory Mark Krein Fredholm operator Schatten class M. G. Krein
Link from a Wikipage to an external page	https://zenodo.org/record/1447421
sameAs	Symmetrizable compact operator Symmetrizable compact operator Symmetrizable compact operator
dbp:wikiPageUsesTemplate	dbt:Citation dbt:Harvtxt dbt:Reflist dbt:Short_description
has 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. (en)
gold:hypernym	Operator
prov:wasDerivedFrom	wikipedia-en:Symmetrizable_compact_operator?oldid=1117757215&ns=0
page length (characters) of wiki page	8956 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Symmetrizable_compact_operator
is rdfs:seeAlso of	Neumann–Poincaré operator
is Link from a Wikipage to another Wikipage of	Leon Lichtenstein Neumann–Poincaré operator
is foaf:primaryTopic of	wikipedia-en:Symmetrizable_compact_operator

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