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Theorems · Theorem · functional analysis

ContinuousLinearMap.isometry_mul

∀ (𝕜 : Type u_1) [inst : NontriviallyNormedField 𝕜] (R : Type u_3) [inst_1 : NonUnitalSeminormedRing R]
  [inst_2 : NormedSpace 𝕜 R] [inst_3 : IsScalarTower 𝕜 R R] [inst_4 : SMulCommClass 𝕜 R R] [RegularNormedAlgebra 𝕜 R],
  Isometry ⇑(ContinuousLinearMap.mul 𝕜 R)
Defined in
Mathlib.Analysis.Normed.Operator.Mul
Cited by
4 results in Mathlib
Foundations
Depth 178 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
NontriviallyNormedFieldNonUnitalSeminormedRingNormedSpaceIsScalarTowerSMulCommClassRegularNormedAlgebra
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

ContinuousLinearMap.opNorm_mul_apply · cited by 3ContinuousLinearMap.opNor…Unitization.antilipschitzWith_addEquiv · cited by 2Unitization.antilipschitz…Unitization.lipschitzWith_addEquiv · cited by 2Unitization.lipschitzWith…Unitization.splitMul_injective · cited by 0Unitization.splitMul_inje…DFunLike.coe · cited by 62936DFunLike.coeRingHom.id · cited by 18349RingHom.idNormedSpace · cited by 12499NormedSpaceNontriviallyNormedField · cited by 8742NontriviallyNormedFieldContinuousLinearMap · cited by 5352ContinuousLinearMapIsScalarTower · cited by 3896IsScalarTowerSMulCommClass · cited by 1927SMulCommClassIsometry · cited by 230IsometryContinuousLinearMap.mul · cited by 63ContinuousLinearMap.mulNonUnitalSeminormedRing · cited by 44NonUnitalSeminormedRingRegularNormedAlgebra · cited by 26RegularNormedAlgebraRegularNormedAlgebra.isometry_mul' · cited by 1RegularNormedAlgebra.isom…ContinuousLinearMap.isometry_…CITED BYCITES

Cites12

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Cited by4

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