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In mathematics, a semi-Hilbert space is a generalization of a Hilbert space in functional analysis, in which, roughly speaking, the inner product is required only to be positive semi-definite rather than positive definite, so that it gives rise to a seminorm rather than a vector space norm. The quotient of this space by the kernel of this seminorm is also required to be a Hilbert space in the usual sense.

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  • Duon-hilberta spaco (eo)
  • Semi-Hilbert space (en)
  • Semi-Hilbertrum (sv)
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  • En matematiko, duon-hilberta spaco estas ĝeneraligo de hilberta spaco en . En duon-hilberta spaco la estas postulita nur al esti pozitive duon-difinita sed ne pozitive difinita, tiel ke ĝi donas la duonnormon sed ne normon. La de ĉi tiu spaco per la kerno de ĉi tiu duonnorma estas ankaŭ postulita al esti hilberta spaco en la kutima senco. (eo)
  • In mathematics, a semi-Hilbert space is a generalization of a Hilbert space in functional analysis, in which, roughly speaking, the inner product is required only to be positive semi-definite rather than positive definite, so that it gives rise to a seminorm rather than a vector space norm. The quotient of this space by the kernel of this seminorm is also required to be a Hilbert space in the usual sense. (en)
  • Semi-Hilbertrum är inom matematiken en generalisering av Hilbertrum i funktionalanalys, där – grovt räknat – den inre produkten endast behöver vara snarare än , så att det ger upphov till en seminorm snarare än ett vektorrumsnorm. Kvoten av detta rum av kärnan i denna seminorm krävs också för att vara ett Hilbertrum i vanlig mening. (sv)
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  • En matematiko, duon-hilberta spaco estas ĝeneraligo de hilberta spaco en . En duon-hilberta spaco la estas postulita nur al esti pozitive duon-difinita sed ne pozitive difinita, tiel ke ĝi donas la duonnormon sed ne normon. La de ĉi tiu spaco per la kerno de ĉi tiu duonnorma estas ankaŭ postulita al esti hilberta spaco en la kutima senco. (eo)
  • In mathematics, a semi-Hilbert space is a generalization of a Hilbert space in functional analysis, in which, roughly speaking, the inner product is required only to be positive semi-definite rather than positive definite, so that it gives rise to a seminorm rather than a vector space norm. The quotient of this space by the kernel of this seminorm is also required to be a Hilbert space in the usual sense. (en)
  • Semi-Hilbertrum är inom matematiken en generalisering av Hilbertrum i funktionalanalys, där – grovt räknat – den inre produkten endast behöver vara snarare än , så att det ger upphov till en seminorm snarare än ett vektorrumsnorm. Kvoten av detta rum av kärnan i denna seminorm krävs också för att vara ett Hilbertrum i vanlig mening. (sv)
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