Theorems · Theorem · functional analysis
CStarRing.of_le_norm_mul_star_self
∀ {E : Type u_2} [inst : NonUnitalNormedRing E] [inst_1 : StarRing E],
(∀ (x : E), ‖x‖ * ‖x‖ ≤ ‖x * star x‖) → CStarRing E- Defined in
- Mathlib.Analysis.CStarAlgebra.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 117 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NonUnitalNormedRingStarRing
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Cites18
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
- Norm.normstatement and proof · cited by 5,413
- LE.le.transproof · cited by 3,151
- mul_commproof · cited by 2,262
- StarRingstatement and proof · cited by 1,686
- Star.starstatement and proof · cited by 1,082
- norm_zeroproof · cited by 366
- NonUnitalNormedRingstatement and proof · cited by 231
- Function.Surjective.forallproof · cited by 214
- star_starproof · cited by 135
- CStarRingstatement · cited by 61
- NormedStarGroupproof · cited by 54
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