Theorems · Theorem · functional analysis
StarSubalgebra.mem_spectrum_iff
∀ {A : Type u_1} [inst : CStarAlgebra A] (S : StarSubalgebra ℂ A) [hS : IsClosed ↑S] {a : ↥S} {z : ℂ},
z ∈ spectrum ℂ a ↔ z ∈ spectrum ℂ ↑a- Defined in
- Mathlib.Analysis.CStarAlgebra.Spectrum
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 185 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CStarAlgebraIsClosed
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- SetLike.coestatement and proof · cited by 8,199
- Complexstatement and proof · cited by 5,565
- IsClosedstatement and proof · cited by 1,639
- spectrumstatement · cited by 510
- StarSubalgebrastatement and proof · cited by 194
- not_iff_notproof · cited by 159
- CStarAlgebrastatement and proof · cited by 123
- StarSubalgebra.coe_isUnitproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- StarSubalgebra.spectrum_eqproof · cited by 1