Theorems · Theorem · functional analysis
SpectrumRestricts.smul_of_nonneg
∀ {A : Type u_2} [inst : Ring A] [inst_1 : Algebra ℝ A] {a : A},
SpectrumRestricts a ⇑ContinuousMap.realToNNReal →
∀ {r : ℝ}, 0 ≤ r → SpectrumRestricts (r • a) ⇑ContinuousMap.realToNNReal- Cited by
- 1 results in Mathlib
- Foundations
- Depth 168 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites27
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
- Setproof · cited by 53,352
- Realstatement and proof · cited by 25,697
- Algebrastatement and proof · cited by 11,388
- Ringstatement and proof · cited by 7,463
- NNRealstatement · cited by 4,310
- Unitsproof · cited by 2,804
- ContinuousMapstatement · cited by 2,491
- Nontrivialproof · cited by 2,416
- MulZeroClass.mul_zeroproof · cited by 2,091
- Units.valproof · cited by 1,966
- zero_smulproof · cited by 716
Cited by1
Results whose statement or proof uses this declaration.
- spectrum_star_mul_self_nonnegproof · cited by 1