Theorems · Theorem · functional analysis
CStarAlgebra.le_nnnorm_of_mem_quasispectrum
∀ {A : Type u_1} [inst : NonUnitalCStarAlgebra A] {a : A} {x : NNReal}, x ∈ quasispectrum NNReal a → x ≤ ‖a‖₊- Defined in
- Mathlib.Analysis.CStarAlgebra.Spectrum
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 194 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NonUnitalCStarAlgebra
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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 · cited by 25,697
- Complexproof · cited by 5,565
- NNRealstatement and proof · cited by 4,310
- NNNorm.nnnormstatement · cited by 952
- quasispectrumstatement and proof · cited by 292
- NonUnitalCStarAlgebrastatement and proof · cited by 149
- Unitization.quasispectrum_eq_spectrum_inr'proof · cited by 12
- Unitization.nnnorm_inrproof · cited by 2
- spectrum.le_nnnorm_of_memproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- CStarAlgebra.directedOn_nonneg_ballproof · cited by 1