Theorems · Theorem · functional analysis
PositiveLinearMap.exists_norm_apply_le
∀ {A₁ : Type u_1} {A₂ : Type u_2} [inst : NonUnitalCStarAlgebra A₁] [inst_1 : NonUnitalCStarAlgebra A₂]
[inst_2 : PartialOrder A₁] [StarOrderedRing A₁] [inst_4 : PartialOrder A₂] [StarOrderedRing A₂] (f : A₁ →ₚ[ℂ] A₂),
∃ C, ∀ (a : A₁), ‖f a‖ ≤ ↑C * ‖a‖If f is a positive map, then it is bounded (and therefore continuous).
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 322 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites68
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Realstatement and proof · cited by 25,697
- PartialOrderstatement and proof · cited by 6,410
- Complexstatement and proof · cited by 5,565
- Norm.normstatement and proof · cited by 5,413
- Finset.sumproof · cited by 5,195
- NNRealstatement and proof · cited by 4,310
- mul_oneproof · cited by 3,885
- Finset.univproof · cited by 3,473
- LE.le.transproof · cited by 3,151
- one_mulproof · cited by 2,841
- Nat.cast_oneproof · cited by 2,501
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.