Theorems · Theorem · functional analysis
quasispectrum_eq_spectrum_union_zero
∀ (R : Type u_3) {A : Type u_4} [inst : Semifield R] [inst_1 : Ring A] [inst_2 : Algebra R A] (a : A),
quasispectrum R a = spectrum R a ∪ {0}- Cited by
- 8 results in Mathlib
- Foundations
- Depth 45 from the axioms · uses propext, Classical.choice, Quot.sound
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 and proof · cited by 53,352
- Algebrastatement and proof · cited by 11,388
- Ringstatement and proof · cited by 7,463
- Set.ofPredproof · cited by 6,101
- IsUnitproof · cited by 1,602
- spectrumstatement and proof · cited by 510
- Semifieldstatement and proof · cited by 439
- quasispectrumstatement and proof · cited by 292
- quasispectrum_eq_spectrum_unionproof · cited by 3
Cited by8
Results whose statement or proof uses this declaration.
- Unitization.quasispectrum_eq_spectrum_inr'proof · cited by 12
- mem_quasispectrum_iffproof · cited by 2
- Unitization.quasispectrum_inr_eqproof · cited by 2
- NonnegSpectrumClass.iff_spectrum_nonnegproof · cited by 1
- SpectrumRestricts.of_spectrum_eqproof · cited by 0
- isClosedEmbedding_cfcₙHom_of_cfcHomproof · cited by 0
- cfcₙHom_of_cfcHom_injectiveproof · cited by 0
- cfcₙHom_of_cfcHom_map_quasispectrumproof · cited by 0