Theorems · Definition · functional analysis
WithLp.linearEquiv
(p : ENNReal) →
(K : Type u_1) →
(V : Type u_4) → [inst : Semiring K] → [inst_1 : AddCommGroup V] → [inst_2 : Module K V] → WithLp p V ≃ₗ[K] VWithLp.equiv as a linear equivalence.
- Defined in
- Mathlib.Analysis.Normed.Lp.WithLp
- Cited by
- 29 results in Mathlib
- Foundations
- Depth 110 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemiringAddCommGroupModule
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- AddCommGroupstatement and proof · cited by 12,871
- ENNRealstatement and proof · cited by 9,879
- LinearEquivstatement · cited by 3,317
- AddEquivproof · cited by 1,087
- WithLpstatement and proof · cited by 345
- Equiv.toFunproof · cited by 279
- AddEquiv.toEquivproof · cited by 174
- Equiv.invFunproof · cited by 163
- WithLp.addEquivproof · cited by 14
Cited by52
Results whose statement or proof uses this declaration.
- OrthonormalBasis.toBasisproof · cited by 102
- PiLp.continuousLinearEquivproof · cited by 31
- WithLp.prodContinuousLinearEquivproof · cited by 15
- Submodule.orthogonalDecompositionproof · cited by 14
- Matrix.toLpLinproof · cited by 14
- PiLp.basisFunproof · cited by 12
- WithLp.linearEquiv_symm_applystatement and proof · cited by 11
- LinearIsometryEquiv.piLpCongrLeftproof · cited by 7
- finrank_euclideanSpaceproof · cited by 7
- NumberField.mixedEmbedding.euclidean.toMixedproof · cited by 6
- Submodule.orthogonalDecomposition_applyproof · cited by 6
- Quaternion.linearIsometryEquivTupleproof · cited by 6