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Theorems · Theorem · functional analysis

Filter.IsIncreasingApproximateUnit.eventually_norm

∀ {A : Type u_1} [inst : NonUnitalCStarAlgebra A] [inst_1 : PartialOrder A] {l : Filter A},
  l.IsIncreasingApproximateUnit → ∀ᶠ (x : A) in l, ‖x‖ ≤ 1
Defined in
Mathlib.Analysis.CStarAlgebra.ApproximateUnit
Cited by
2 results in Mathlib
Foundations
Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
NonUnitalCStarAlgebraPartialOrder
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Filter.IsIncreasingApproximateUnit.closedBall_mem · cited by 0IsIncreasingApproximateUn…Filter.IsIncreasingApproximateUnit.eventually_nnnorm · cited by 0IsIncreasingApproximateUn…Real · cited by 25697RealFilter · cited by 8121FilterPartialOrder · cited by 6410PartialOrderNorm.norm · cited by 5413Norm.normFilter.Eventually · cited by 3134Filter.EventuallyNonUnitalCStarAlgebra · cited by 149NonUnitalCStarAlgebraFilter.IsIncreasingApproximateUnit · cited by 9Filter.IsIncreasingApprox…IsIncreasingApproximateUnit.e…CITED BYCITES

Cites7

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by2

Results whose statement or proof uses this declaration.