Theorems · Theorem · functional analysis
CFC.concaveOn_nnrpow
∀ {A : Type u_1} [inst : NonUnitalCStarAlgebra A] [inst_1 : PartialOrder A] [inst_2 : StarOrderedRing A] {p : NNReal},
p ∈ Set.Icc 0 1 → ConcaveOn ℝ (Set.Ici 0) fun a => a ^ pa ↦ a ^ p is operator concave for p ∈ [0,1].
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 329 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites23
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Realstatement and proof · cited by 25,697
- PartialOrderstatement and proof · cited by 6,410
- Complexstatement · cited by 5,565
- NNRealstatement and proof · cited by 4,310
- Set.extproof · cited by 2,266
- Set.Iccstatement and proof · cited by 1,702
- Set.Iooproof · cited by 1,214
- Set.Icistatement and proof · cited by 1,070
- StarOrderedRingstatement and proof · cited by 587
- ConcaveOnstatement and proof · cited by 159
- NonUnitalCStarAlgebrastatement and proof · cited by 149
Cited by2
Results whose statement or proof uses this declaration.
- CFC.concaveOn_rpowproof · cited by 1
- CFC.concaveOn_sqrtproof · cited by 0