| dbo: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) |
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dbr:Hermitian_form dbr:Definite_bilinear_form dbc:Topological_vector_spaces dbr:Vector_space dbc:Operator_theory dbr:Mathematics dbr:Operator_(mathematics) dbr:Endomorphism dbr:Lorentz_invariance dbr:Closed_set dbr:Functional_analysis dbr:Spectrum_(functional_analysis) dbr:Topology dbr:USSR dbr:Linear_subspace dbr:Continuity_(topology) dbr:Projection_(linear_algebra) dbr:Quotient_space_(topology) dbr:Hilbert_space dbr:Inner_product dbr:Normed_vector_space dbr:Lev_Semenovich_Pontryagin dbr:Direct_sum_of_vector_spaces dbr:Mark_Grigorievich_Krein dbr:Majorant_topology |
| dbp:first |
H. (en) B.S. (en) N.K. (en) |
| dbp:id |
h/h047390 (en) k/k055840 (en) p/p073800 (en) |
| dbp:last |
Langer (en) Pavlov (en) Nikol'skii (en) |
| dbp:title |
Hilbert space with an indefinite metric (en) Krein space (en) Pontryagin space (en) |
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dbt:ISBN dbt:Issn dbt:Eom |
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dbc:Topological_vector_spaces dbc:Operator_theory |
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| 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) |
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Kreinraum (de) Indefinite inner product space (en) |
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