Theorems · Theorem · functional analysis

CStarAlgebra.norm_or_neg_norm_mem_spectrum

∀ {A : Type u_1} [inst : CStarAlgebra A] [Nontrivial A] {a : A},
  autoParam (IsSelfAdjoint a) CStarAlgebra.norm_or_neg_norm_mem_spectrum._auto_1 →
    ‖a‖ ∈ spectrum ℝ a ∨ -‖a‖ ∈ spectrum ℝ a

Defined in: Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Order
Cited by: 1 results in Mathlib
Foundations: Depth 312 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CStarAlgebra Nontrivial

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Cites16

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

DFunLike.coeproof · cited by 62,936
Setstatement · cited by 53,352
Realstatement and proof · cited by 25,697
Norm.normstatement · cited by 5,413
Nontrivialstatement and proof · cited by 2,416
IsSelfAdjointstatement and proof · cited by 545
spectrumstatement and proof · cited by 510
CStarAlgebrastatement and proof · cited by 123
Set.Nonempty.imageproof · cited by 87
SpectrumRestrictsproof · cited by 51
Complex.reCLMproof · cited by 46
IsSelfAdjoint.spectrumRestrictsproof · cited by 13

Cited by1

Results whose statement or proof uses this declaration.

selfAdjoint.norm_sq_expUnitary_sub_oneproof · cited by 3