Theorems · Theorem · functional analysis
spectrum.of_subsingleton
∀ {R : Type u} {A : Type v} [inst : CommSemiring R] [inst_1 : Ring A] [inst_2 : Algebra R A] [Subsingleton A] (a : A),
spectrum R a = ∅- Defined in
- Mathlib.Algebra.Algebra.Spectrum.Basic
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 58 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- Ringstatement and proof · cited by 7,463
- Compl.complproof · cited by 2,925
- spectrumstatement · cited by 510
- Set.compl_univproof · cited by 41
- spectrum.resolventSet_of_subsingletonproof · cited by 1
Cited by10
Results whose statement or proof uses this declaration.
- norm_apply_le_norm_cfcproof · cited by 5
- CStarAlgebra.norm_le_iff_le_algebraMapproof · cited by 5
- apply_le_nnnorm_cfc_nnrealproof · cited by 3
- spectrum.map_polynomial_aeval_of_nonemptyproof · cited by 2
- Unitary.norm_sub_one_sq_eqproof · cited by 2
- Unitary.spectrum_subset_circleproof · cited by 2
- spectrum.SpectralRadius.of_subsingletonproof · cited by 2
- IsIdempotentElem.spectrum_subsetproof · cited by 2
- SpectrumRestricts.smul_of_nonnegproof · cited by 1
- Unitary.norm_sub_one_lt_two_iffproof · cited by 1