Theorems · Theorem · functional analysis
IsSelfAdjoint.le_algebraMap_norm_self
∀ {A : Type u_1} [inst : CStarAlgebra A] [inst_1 : PartialOrder A] [StarOrderedRing A] {a : A},
autoParam (IsSelfAdjoint a) IsSelfAdjoint.le_algebraMap_norm_self._auto_1 → a ≤ (algebraMap ℝ A) ‖a‖- Cited by
- 7 results in Mathlib
- Foundations
- Depth 311 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Realstatement and proof · cited by 25,697
- RingHomstatement · cited by 10,189
- PartialOrderstatement and proof · cited by 6,410
- Norm.normstatement · cited by 5,413
- Algebra.algebraMapstatement · cited by 4,706
- Nontrivialproof · cited by 2,416
- StarOrderedRingstatement and proof · cited by 587
- IsSelfAdjointstatement and proof · cited by 545
- spectrumproof · cited by 510
- CStarAlgebrastatement and proof · cited by 123
- Real.le_norm_selfproof · cited by 16
Cited by7
Results whose statement or proof uses this declaration.
- CStarAlgebra.norm_le_norm_of_nonneg_of_leproof · cited by 6
- CStarAlgebra.star_left_conjugate_le_norm_smulproof · cited by 1
- PositiveLinearMap.norm_apply_le_of_nonnegproof · cited by 0
- IsSelfAdjoint.neg_algebraMap_norm_le_selfproof · cited by 0
- CStarAlgebra.star_mul_le_algebraMap_norm_sqproof · cited by 0
- PositiveLinearMap.apply_le_of_isSelfAdjointproof · cited by 0
- CStarAlgebra.mul_star_le_algebraMap_norm_sqproof · cited by 0