Theorems · Theorem · commutative algebra
isNonarchimedean_spectralNorm_of_finiteDimensional_normal
∀ (K : Type u_2) [inst : NormedField K] (L : Type u_3) [inst_1 : Field L] [inst_2 : Algebra K L] [h_fin : FiniteDimensional K L] [hn : Normal K L] [IsUltrametricDist K], IsNonarchimedean (spectralNorm K L)
The spectral norm is nonarchimedean when L/K is finite and normal.
See also isNonarchimedean_spectralNorm for a more general result.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 220 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- Algebrastatement and proof · cited by 11,388
- Fieldstatement and proof · cited by 7,404
- FiniteDimensionalstatement and proof · cited by 1,854
- NormedFieldstatement and proof · cited by 1,084
- IsUltrametricDiststatement and proof · cited by 177
- Normalstatement and proof · cited by 92
- IsNonarchimedeanstatement and proof · cited by 77
- spectralNormstatement · cited by 31
- spectralNorm_eq_invariantExtensionproof · cited by 3
- IsUltrametricDist.isNonarchimedean_invariantExtensionproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- isNonarchimedean_spectralNormproof · cited by 1