About: Schatten class operator

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In mathematics, specifically functional analysis, a pth Schatten-class operator is a bounded linear operator on a Hilbert space with finite pth Schatten norm. The space of pth Schatten-class operators is a Banach space with respect to the Schatten norm. Via polar decomposition, one can prove that the space of pth Schatten class operators is an ideal in B(H). Furthermore, the Schatten norm satisfies a type of Hölder inequality: Observe that the 2nd Schatten class is in fact the Hilbert space of Hilbert–Schmidt operators. Moreover, the 1st Schatten class is the space of trace class operators.

Attributes	Values
rdf:type	yago:Abstraction100002137 yago:Possession100032613 yago:Property113244109 yago:Relation100031921 yago:WikicatPropertiesOfTopologicalSpaces
rdfs:label	Schatten-Klasse (de) シャッテンクラス作用素 (ja) Schatten class operator (en)
rdfs:comment	Die Schatten-Klassen, auch Schatten-von-Neumann-Klassen, benannt nach Robert Schatten und John von Neumann, sind spezielle Algebren von Operatoren, die im mathematischen Teilgebiet der Funktionalanalysis untersucht werden. Sie haben viele Eigenschaften mit den Folgenräumen gemeinsam. (de) In mathematics, specifically functional analysis, a pth Schatten-class operator is a bounded linear operator on a Hilbert space with finite pth Schatten norm. The space of pth Schatten-class operators is a Banach space with respect to the Schatten norm. Via polar decomposition, one can prove that the space of pth Schatten class operators is an ideal in B(H). Furthermore, the Schatten norm satisfies a type of Hölder inequality: Observe that the 2nd Schatten class is in fact the Hilbert space of Hilbert–Schmidt operators. Moreover, the 1st Schatten class is the space of trace class operators. (en)
dcterms:subject	Operator theory
Wikipage page ID	10698304 (xsd:integer)
Wikipage revision ID	1025150817 (xsd:integer)
Link from a Wikipage to another Wikipage	Operator theory Mathematics Operator norm Compact operator Functional analysis Banach space Hilbert–Schmidt operator Hilbert space Trace class Polar decomposition Schatten norm Hölder inequality Bounded linear operator
sameAs	Schatten class operator Schatten class operator Schatten class operator Schatten class operator Schatten class operator Schatten class operator
dbp:wikiPageUsesTemplate	dbt:Unreferenced
has abstract	Die Schatten-Klassen, auch Schatten-von-Neumann-Klassen, benannt nach Robert Schatten und John von Neumann, sind spezielle Algebren von Operatoren, die im mathematischen Teilgebiet der Funktionalanalysis untersucht werden. Sie haben viele Eigenschaften mit den Folgenräumen gemeinsam. (de) In mathematics, specifically functional analysis, a pth Schatten-class operator is a bounded linear operator on a Hilbert space with finite pth Schatten norm. The space of pth Schatten-class operators is a Banach space with respect to the Schatten norm. Via polar decomposition, one can prove that the space of pth Schatten class operators is an ideal in B(H). Furthermore, the Schatten norm satisfies a type of Hölder inequality: If we denote by the Banach space of compact operators on H with respect to the operator norm, the above Hölder-type inequality even holds for . From this it follows that , is a well-defined contraction. (Here the prime denotes (topological) dual.) Observe that the 2nd Schatten class is in fact the Hilbert space of Hilbert–Schmidt operators. Moreover, the 1st Schatten class is the space of trace class operators. (en)
prov:wasDerivedFrom	wikipedia-en:Schatten_class_operator?oldid=1025150817&ns=0
page length (characters) of wiki page	1277 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Schatten_class_operator
is Link from a Wikipage to another Wikipage of	Robert Schatten Commutator subspace Oscillator representation Calkin correspondence Singular trace Schatten class Reflexive space Schatten norm Weyl–von Neumann theorem
is Wikipage redirect of	Schatten class
is known for of	Robert Schatten
is known for of	Robert Schatten
is foaf:primaryTopic of	wikipedia-en:Schatten_class_operator

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