Theorems · Theorem · functional analysis
CStarModule.norm_zero_iff
∀ (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] [CStarModule A E] (x : E), ‖x‖ = 0 ↔ x = 0- Cited by
- 1 results in Mathlib
- Foundations
- Depth 167 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · 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.innerproof · cited by 1,089
- Real.sqrtproof · cited by 545
- Normstatement and proof · cited by 512
- norm_zeroproof · cited by 366
- NonUnitalSemiringproof · cited by 339
Cited by1
Results whose statement or proof uses this declaration.
- CStarModule.normedSpaceCoreproof · cited by 1