Theorems · Theorem · functional analysis
IsCoercive.isClosed_range
∀ {V : Type u} [inst : NormedAddCommGroup V] [inst_1 : InnerProductSpace ℝ V] [inst_2 : CompleteSpace V]
{B : V →L[ℝ] V →L[ℝ] ℝ}, IsCoercive B → IsClosed ↑(↑(InnerProductSpace.continuousLinearMapOfBilin B)).range- Cited by
- 0 results in Mathlib
- Foundations
- Depth 189 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Realstatement and proof · cited by 25,697
- RingHom.idstatement and proof · cited by 18,349
- NormedAddCommGroupstatement and proof · cited by 15,752
- SetLike.coestatement · cited by 8,199
- Submodulestatement · cited by 7,192
- ContinuousLinearMapstatement and proof · cited by 5,352
- NNRealproof · cited by 4,310
- InnerProductSpacestatement and proof · cited by 3,523
- CompleteSpacestatement and proof · cited by 2,532
- IsClosedstatement · cited by 1,639
- LinearMap.rangestatement · cited by 893
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