Theorems · Theorem · functional analysis
IsSelfAdjoint.nnnorm_sum_eq_sup
∀ {A : Type u_1} [inst : NonUnitalCStarAlgebra A] {ι : Type u_2} {f : ι → A} (s : Finset ι),
(∀ i ∈ s, IsSelfAdjoint (f i)) →
Pairwise (Function.onFun (fun x1 x2 => x1 * x2 = 0) f) → ‖∑ i ∈ s, f i‖₊ = s.sup fun x => ‖f x‖₊- Cited by
- 0 results in Mathlib
- Foundations
- Depth 310 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NonUnitalCStarAlgebra
Around this declaration
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Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement and proof · cited by 13,712
- Finset.sumstatement and proof · cited by 5,195
- NNRealstatement · cited by 4,310
- NNNorm.nnnormstatement and proof · cited by 952
- Function.onFunstatement and proof · cited by 570
- IsSelfAdjointstatement and proof · cited by 545
- Finset.supstatement and proof · cited by 530
- Pairwisestatement and proof · cited by 516
- Finset.sum_insertproof · cited by 196
- Finset.mul_sumproof · cited by 196
- NonUnitalCStarAlgebrastatement and proof · cited by 149
- Finset.sum_eq_zeroproof · cited by 139
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