Theorems · Theorem · functional analysis
mulLeft_bound
∀ {α : Type u_2} [inst : NonUnitalSeminormedRing α] (x y : α), ‖(AddMonoidHom.mulLeft x) y‖ ≤ ‖x‖ * ‖y‖In a seminormed ring, the left-multiplication AddMonoidHom is bounded.
- Defined in
- Mathlib.Analysis.Normed.Ring.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NonUnitalSeminormedRing
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Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Realstatement · cited by 25,697
- Norm.normstatement · cited by 5,413
- AddMonoidHomstatement · cited by 3,230
- NonUnitalSeminormedRingstatement and proof · cited by 44
- norm_mul_leproof · cited by 31
- AddMonoidHom.mulLeftstatement · cited by 23
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