Theorems · Theorem · functional analysis

NonUnitalIsometricContinuousFunctionalCalculus.isGreatest_quasispectrum

∀ {A : Type u_1} [inst : NonUnitalNormedRing A] [inst_1 : StarRing A] [inst_2 : NormedSpace ℝ A]
  [inst_3 : IsScalarTower ℝ A A] [inst_4 : SMulCommClass ℝ A A] [inst_5 : PartialOrder A] [StarOrderedRing A]
  [NonUnitalIsometricContinuousFunctionalCalculus ℝ A IsSelfAdjoint] [NonnegSpectrumClass ℝ A] (a : A),
  autoParam (0 ≤ a) NonUnitalIsometricContinuousFunctionalCalculus.isGreatest_quasispectrum._auto_1 →
    IsGreatest (quasispectrum NNReal a) ‖a‖₊

Defined in: Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Isometric
Cited by: 1 results in Mathlib
Foundations: Depth 200 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: NonUnitalNormedRing StarRing NormedSpace IsScalarTower SMulCommClass PartialOrder StarOrderedRing NonUnitalIsometricContinuousFunctionalCalculus NonnegSpectrumClass

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Cites20

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
NormedSpacestatement and proof · cited by 12,499
PartialOrderstatement and proof · cited by 6,410
NNRealstatement and proof · cited by 4,310
IsScalarTowerstatement and proof · cited by 3,896
SMulCommClassstatement and proof · cited by 1,927
StarRingstatement and proof · cited by 1,686
NNNorm.nnnormstatement and proof · cited by 952
StarOrderedRingstatement and proof · cited by 587
IsSelfAdjointstatement and proof · cited by 545
Set.image_congrproof · cited by 533
quasispectrumstatement and proof · cited by 292

Cited by1

Results whose statement or proof uses this declaration.

MonotoneOn.nnnorm_cfcₙproof · cited by 1