Theorems · Theorem · functional analysis
CStarMatrix.norm_le_of_forall_inner_le
∀ {m : Type u_1} {n : Type u_2} {A : Type u_5} [inst : Fintype m] [inst_1 : NonUnitalCStarAlgebra A]
[inst_2 : PartialOrder A] [inst_3 : StarOrderedRing A] [inst_4 : Fintype n] {M : CStarMatrix m n A} {C : NNReal},
(∀ (v : WithCStarModule A (m → A)) (w : WithCStarModule A (n → A)),
‖inner A w ((CStarMatrix.toCLM M) v)‖ ≤ ↑C * ‖v‖ * ‖w‖) →
‖M‖ ≤ ↑C- Cited by
- 0 results in Mathlib
- Foundations
- Depth 337 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites28
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
- Moduleproof · cited by 20,661
- RingHom.idstatement · cited by 18,349
- AddCommGroupproof · cited by 12,871
- LinearMapstatement · cited by 10,215
- Fintypestatement and proof · cited by 7,736
- PartialOrderstatement and proof · cited by 6,410
- Complexstatement and proof · cited by 5,565
- Norm.normstatement and proof · cited by 5,413
- ContinuousLinearMapstatement · cited by 5,352
- NNRealstatement and proof · cited by 4,310
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.