Theorems · Theorem · functional analysis
CStarModule.norm_inner_le
∀ {A : Type u_1} (E : Type u_2) [inst : NonUnitalCStarAlgebra A] [inst_1 : PartialOrder A] [inst_2 : AddCommGroup E]
[inst_3 : Module ℂ E] [inst_4 : SMul A E] [inst_5 : Norm E] [inst_6 : CStarModule A E] [StarOrderedRing A] {x y : E},
‖inner A x y‖ ≤ ‖x‖ * ‖y‖The Cauchy-Schwarz inequality for Hilbert C⋆-modules.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 321 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites29
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- PartialOrderstatement and proof · cited by 6,410
- Complexstatement and proof · cited by 5,565
- Norm.normstatement and proof · cited by 5,413
- StarRingproof · cited by 1,686
- Inner.innerstatement and proof · cited by 1,089
- norm_nonnegproof · cited by 725
- StarOrderedRingstatement and proof · cited by 587
- Normstatement and proof · cited by 512
- mul_nonnegproof · cited by 397
Cited by2
Results whose statement or proof uses this declaration.
- CStarModule.norm_triangleproof · cited by 1
- CStarModule.norm_eq_csSupproof · cited by 0