Theorems · Definition · functional analysis
ContinuousLinearMap.mul
(𝕜 : Type u_1) →
[inst : NontriviallyNormedField 𝕜] →
(R : Type u_3) →
[inst_1 : NonUnitalSeminormedRing R] →
[inst_2 : NormedSpace 𝕜 R] → [IsScalarTower 𝕜 R R] → [SMulCommClass 𝕜 R R] → R →L[𝕜] R →L[𝕜] RMultiplication in a non-unital normed algebra as a continuous bilinear map.
- Defined in
- Mathlib.Analysis.Normed.Operator.Mul
- Cited by
- 63 results in Mathlib
- Foundations
- Depth 176 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- RingHom.idstatement · cited by 18,349
- NormedSpacestatement and proof · cited by 12,499
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- ContinuousLinearMapstatement · cited by 5,352
- IsScalarTowerstatement and proof · cited by 3,896
- SMulCommClassstatement and proof · cited by 1,927
- LinearMap.mulproof · cited by 61
- NonUnitalSeminormedRingstatement and proof · cited by 44
- LinearMap.mkContinuous₂proof · cited by 5
Cited by70
Results whose statement or proof uses this declaration.
- ContinuousLinearMap.mulLeftRightproof · cited by 16
- Unitization.norm_inrproof · cited by 8
- HasFDerivWithinAt.mul'proof · cited by 7
- HasFDerivAt.mul'proof · cited by 5
- PositiveLinearMap.leftMulMapPreGNSproof · cited by 4
- DoubleCentralizer.coeproof · cited by 4
- HasStrictFDerivAt.mul'proof · cited by 4
- Unitization.norm_eq_supstatement and proof · cited by 4
- HasFDerivWithinAt.mul_const'proof · cited by 4
- ContinuousLinearMap.isometry_mulstatement · cited by 4
- HasFDerivAt.const_mulproof · cited by 4
- HasFDerivAt.mul_const'proof · cited by 3