Theorems · Definition · functional analysis

LinearIsometryEquiv.toLinearEquiv

{R : Type u_1} →
  {R₂ : Type u_2} →
    [inst : Semiring R] →
      [inst_1 : Semiring R₂] →
        {σ₁₂ : R →+* R₂} →
          {σ₂₁ : R₂ →+* R} →
            [inst_2 : RingHomInvPair σ₁₂ σ₂₁] →
              [inst_3 : RingHomInvPair σ₂₁ σ₁₂] →
                {E : Type u_11} →
                  {E₂ : Type u_12} →
                    [inst_4 : SeminormedAddCommGroup E] →
                      [inst_5 : SeminormedAddCommGroup E₂] →
                        [inst_6 : Module R E] → [inst_7 : Module R₂ E₂] → (E ≃ₛₗᵢ[σ₁₂] E₂) → E ≃ₛₗ[σ₁₂] E₂

Defined in

Mathlib.Analysis.Normed.Operator.LinearIsometry

Cited by

107 results in Mathlib

Foundations

Depth 13 from the axioms, rests on 94 definitions · uses no axioms

Assumes

SemiringSemiringRingHomInvPairRingHomInvPairSeminormedAddCommGroupSeminormedAddCommGroupModuleModule