Theorems · Definition · functional analysis
scalarSMulCLE
(H : Type u_1) → [inst : NormedAddCommGroup H] → [inst_1 : InnerProductSpace ℂ H] → ℂˣ → H ≃L[ℝ] H
the scalar product by a non-zero complex number as a continuous real-linear equivalence.
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 170 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.
- DFunLike.coeproof · cited by 62,936
- Realstatement · cited by 25,697
- RingHom.idstatement · cited by 18,349
- NormedAddCommGroupstatement and proof · cited by 15,752
- Complexstatement and proof · cited by 5,565
- InnerProductSpacestatement and proof · cited by 3,523
- Unitsstatement and proof · cited by 2,804
- ContinuousLinearEquivstatement · cited by 743
- ContinuousLinearEquiv.smulLeftproof · cited by 6
Cited by8
Results whose statement or proof uses this declaration.
- ClosedSubmodule.mulIproof · cited by 16
- ClosedSubmodule.mulI_mulI_eqproof · cited by 2
- ClosedSubmodule.mulI_orthogonal_eq_symplCompproof · cited by 2
- scalarSMulCLE_symm_applystatement · cited by 1
- ClosedSubmodule.mem_symplComp_iffproof · cited by 1
- ClosedSubmodule.mulI_infproof · cited by 1
- ClosedSubmodule.mulI_supproof · cited by 1
- scalarSMulCLE_applystatement · cited by 0