Theorems · Theorem · functional analysis
unitary_iff_isStarNormal_and_spectrum_subset_unitary
∀ {A : Type u_1} [inst : TopologicalSpace A] [inst_1 : Ring A] [inst_2 : StarRing A] [inst_3 : Algebra ℂ A]
[ContinuousFunctionalCalculus ℂ A IsStarNormal] {u : A}, u ∈ unitary A ↔ IsStarNormal u ∧ spectrum ℂ u ⊆ ↑(unitary ℂ)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 166 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
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
- TopologicalSpacestatement and proof · cited by 24,529
- Algebrastatement and proof · cited by 11,388
- SetLike.coestatement and proof · cited by 8,199
- Ringstatement and proof · cited by 7,463
- Complexstatement and proof · cited by 5,565
- Submonoidstatement · cited by 3,086
- StarRingstatement and proof · cited by 1,686
- Star.starproof · cited by 1,082
- starRingEndproof · cited by 671
- spectrumstatement and proof · cited by 510
Cited by2
Results whose statement or proof uses this declaration.
- mem_unitary_of_spectrum_subset_unitaryproof · cited by 0
- spectrum_subset_unitary_of_mem_unitaryproof · cited by 0