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Theorems · Definition · functional analysis

RingHom.IsBounded

{α : Type u_5} → [inst : SeminormedRing α] → {β : Type u_6} → [inst_1 : SeminormedRing β] → (α →+* β) → Prop

A homomorphism f between semi_normed_rings is bounded if there exists a positive constant C such that for all x in α, norm (f x) ≤ C * norm x.

Defined in
Mathlib.Analysis.Normed.Ring.Basic
Cited by
1 results in Mathlib
Foundations
Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
SeminormedRingSeminormedRing
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Around this declaration

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contraction_of_isPowMul · cited by 0contraction_of_isPowMulDFunLike.coe · cited by 62936DFunLike.coeReal · cited by 25697RealRingHom · cited by 10189RingHomNorm.norm · cited by 5413Norm.normSeminormedRing · cited by 446SeminormedRingRingHom.IsBoundedCITED BYCITES

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Cited by1

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