On Inner Products in Linear, Metric Spaces¶
Jordan, P., & Neumann, J. V. (1935). On Inner Products in Linear, Metric Spaces. Annals of Mathematics, 36(3), 719-723.
Cited by¶
1 citation across 1 artifact.
Each citation links to the sentence it supports in the citing article.
Domain-specific¶
- Parallelogram Law
- Jordan and von Neumann proved the characterizing result in 1935: over the real or complex scalars, a norm satisfies the parallelogram law for all vector pairs if and only if there is an inner product whose induced norm is the given norm.
This sourceInstitutional copy: <https://www.mathematik.uni-muenchen.de/~michel/jordan-von_neumann_-_parallelogram_identity.pdf>.
- Jordan and von Neumann proved the characterizing result in 1935: over the real or complex scalars, a norm satisfies the parallelogram law for all vector pairs if and only if there is an inner product whose induced norm is the given norm.
Verification¶
Does it exist? Confirmed. This work's DOI resolves to a registered record, which fixes its identity. That is all it fixes.
Does it back the claim? Not recorded. The single citation of this work carries no recorded support check.
Support is checked per citation rather than per work — the same source can be cited soundly in one article and wrongly in another. Per-citation recording began recently, so a citation with no recorded check is a gap in the record rather than evidence it went unchecked.
See how references were verified.
Registry ID ref:6d86f7273987 · see in the full table