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单词 BanachSpacesWithComplementedSubspaces
释义

Banach spaces with complemented subspaces


Theorem. [Lindenstrauss-Tzafriri]

Let V be a Banach spaceMathworldPlanetmath, such that for each closed subspace M there exists a closed subspace N such that MN=0 and M+N=V (i.e. every closed subspace is complemented). Then V is isomorphic to a Hilbert spaceMathworldPlanetmath (i.e. there exists a Hilbert space structure on V that induces the original topologyMathworldPlanetmath on V as a Banach space).

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更新时间:2025/5/4 22:50:59