Theorems · Definition · functional analysis

ContinuousLinearMap.flip

{𝕜 : Type u_1} →
  {𝕜₂ : Type u_2} →
    {𝕜₃ : Type u_3} →
      {E : Type u_4} →
        {F : Type u_6} →
          {G : Type u_8} →
            [inst : SeminormedAddCommGroup E] →
              [inst_1 : SeminormedAddCommGroup F] →
                [inst_2 : SeminormedAddCommGroup G] →
                  [inst_3 : NontriviallyNormedField 𝕜] →
                    [inst_4 : NontriviallyNormedField 𝕜₂] →
                      [inst_5 : NontriviallyNormedField 𝕜₃] →
                        [inst_6 : NormedSpace 𝕜 E] →
                          [inst_7 : NormedSpace 𝕜₂ F] →
                            [inst_8 : NormedSpace 𝕜₃ G] →
                              {σ₂₃ : 𝕜₂ →+* 𝕜₃} →
                                {σ₁₃ : 𝕜 →+* 𝕜₃} →
                                  [RingHomIsometric σ₂₃] →
                                    [RingHomIsometric σ₁₃] → (E →SL[σ₁₃] F →SL[σ₂₃] G) → F →SL[σ₂₃] E →SL[σ₁₃] G

Flip the order of arguments of a continuous bilinear map. For a version bundled as LinearIsometryEquiv, see ContinuousLinearMap.flipL.

Defined in

Mathlib.Analysis.Normed.Operator.Bilinear

Cited by

128 results in Mathlib

Foundations

Depth 176 from the axioms, rests on 4,242 definitions · uses propext, Classical.choice, Quot.sound

Assumes

SeminormedAddCommGroupSeminormedAddCommGroupSeminormedAddCommGroupNontriviallyNormedFieldNontriviallyNormedFieldNontriviallyNormedFieldNormedSpaceNormedSpaceNormedSpaceRingHomIsometricRingHomIsometric