About: Indefinite inner product space

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In mathematics, in the field of functional analysis, an indefinite inner product space is an infinite-dimensional complex vector space equipped with both an indefinite inner product and a positive semi-definite inner product where the metric operator is an endomorphism of obeying An indefinite inner product space is called a Krein space (or -space) if is positive definite and possesses a . Krein spaces are named in honor of the Soviet mathematician Mark Grigorievich Krein (3 April 1907 – 17 October 1989).

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rdfs:label	Kreinraum (de) Indefinite inner product space (en)
rdfs:comment	In der Funktionalanalysis ist ein Kreinraum (nach Mark Krein) ein Hilbertraum mit einer abgeschwächten Struktur: einem i. A. indefiniten inneren Produkt anstelle des üblichen Skalarprodukts. Eine genaue Definition findet sich weiter unten. In vielen Anwendungen ist die Theorie der Kreinräume ein sehr nützliches Werkzeug, beispielsweise bei oder bei bestimmten Differentialoperatoren. (de) In mathematics, in the field of functional analysis, an indefinite inner product space is an infinite-dimensional complex vector space equipped with both an indefinite inner product and a positive semi-definite inner product where the metric operator is an endomorphism of obeying An indefinite inner product space is called a Krein space (or -space) if is positive definite and possesses a . Krein spaces are named in honor of the Soviet mathematician Mark Grigorievich Krein (3 April 1907 – 17 October 1989). (en)
dcterms:subject	Topological vector spaces Operator theory
Wikipage page ID	5571012 (xsd:integer)
Wikipage revision ID	1088152589 (xsd:integer)
Link from a Wikipage to another Wikipage	Hermitian form Definite bilinear form Topological vector spaces Vector space Operator theory Mathematics Operator (mathematics) Endomorphism Lorentz invariance Closed set Functional analysis Spectrum (functional analysis) Topology USSR Linear subspace Continuity (topology) Projection (linear algebra) Quotient space (topology) Hilbert space Inner product Normed vector space Lev Semenovich Pontryagin Direct sum of vector spaces Mark Grigorievich Krein dbr:Majorant_topology
sameAs	Indefinite inner product space Indefinite inner product space Indefinite inner product space Indefinite inner product space Indefinite inner product space
dbp:wikiPageUsesTemplate	dbt:ISBN dbt:Issn dbt:Eom
first	H. (en) B.S. (en) N.K. (en)
id	h/h047390 (en) k/k055840 (en) p/p073800 (en)
last	Langer (en) Pavlov (en) Nikol'skii (en)
title	Hilbert space with an indefinite metric (en) Krein space (en) Pontryagin space (en)
has abstract	In der Funktionalanalysis ist ein Kreinraum (nach Mark Krein) ein Hilbertraum mit einer abgeschwächten Struktur: einem i. A. indefiniten inneren Produkt anstelle des üblichen Skalarprodukts. Eine genaue Definition findet sich weiter unten. In vielen Anwendungen ist die Theorie der Kreinräume ein sehr nützliches Werkzeug, beispielsweise bei oder bei bestimmten Differentialoperatoren. (de) In mathematics, in the field of functional analysis, an indefinite inner product space is an infinite-dimensional complex vector space equipped with both an indefinite inner product and a positive semi-definite inner product where the metric operator is an endomorphism of obeying The indefinite inner product space itself is not necessarily a Hilbert space; but the existence of a positive semi-definite inner product on implies that one can form a quotient space on which there is a positive definite inner product. Given a strong enough topology on this quotient space, it has the structure of a Hilbert space, and many objects of interest in typical applications fall into this quotient space. An indefinite inner product space is called a Krein space (or -space) if is positive definite and possesses a . Krein spaces are named in honor of the Soviet mathematician Mark Grigorievich Krein (3 April 1907 – 17 October 1989). (en)
prov:wasDerivedFrom	wikipedia-en:Indefinite_inner_product_space?oldid=1088152589&ns=0
page length (characters) of wiki page	11158 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Indefinite_inner_product_space
is Link from a Wikipage to another Wikipage of	Pesonen operator Krein space Indefinite Hilbert space Pontriagin space Pontryagin space Hilbert space with an indefinite metric
is Wikipage redirect of	Pesonen operator Krein space Indefinite Hilbert space Pontriagin space Pontryagin space Hilbert space with an indefinite metric
is foaf:primaryTopic of	wikipedia-en:Indefinite_inner_product_space

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