Theorems · Theorem · functional analysis
ContinuousLinearMap.coe_ofIsClosedGraph
∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_3} [inst_1 : NormedAddCommGroup E]
[inst_2 : NormedSpace 𝕜 E] [inst_3 : CompleteSpace E] {F : Type u_5} [inst_4 : NormedAddCommGroup F]
[inst_5 : NormedSpace 𝕜 F] [inst_6 : CompleteSpace F] {g : E →ₗ[𝕜] F} (hg : IsClosed ↑g.graph),
↑(ContinuousLinearMap.ofIsClosedGraph hg) = g- Defined in
- Mathlib.Analysis.Normed.Operator.Banach
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 174 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- RingHom.idstatement and proof · cited by 18,349
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- LinearMapstatement and proof · cited by 10,215
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- SetLike.coestatement and proof · cited by 8,199
- Submodulestatement · cited by 7,192
- CompleteSpacestatement and proof · cited by 2,532
- IsClosedstatement and proof · cited by 1,639
- LinearMap.extproof · cited by 844
- ContinuousLinearMap.toLinearMapstatement and proof · cited by 528
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