Theorems · Definition · functional analysis

Unitary.mulLeft

(R : Type u_1) →
  (A : Type u_2) →
    [inst : NormedRing A] →
      [inst_1 : StarRing A] →
        [CStarRing A] → [inst_3 : Ring R] → [inst_4 : Module R A] → [SMulCommClass R A A] → ↥(unitary A) →* A ≃ₗᵢ[R] A

Left multiplication by a unitary as a linear isometric equivalence.

Defined in

Mathlib.Analysis.CStarAlgebra.Unitary.Maps

Cited by

7 results in Mathlib

Foundations

Depth 163 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedRingStarRingCStarRingRingModuleSMulCommClass