Theorems · Inductive type · functional analysis

LinearIsometry

{R : Type u_1} →
  {R₂ : Type u_2} →
    [inst : Semiring R] →
      [inst_1 : Semiring R₂] →
        (R →+* R₂) →
          (E : Type u_11) →
            (E₂ : Type u_12) →
              [inst_2 : SeminormedAddCommGroup E] →
                [inst_3 : SeminormedAddCommGroup E₂] → [Module R E] → [Module R₂ E₂] → Type (max u_11 u_12)

A σ₁₂-semilinear isometric embedding of a normed R-module into an R₂-module, denoted as f : E →ₛₗᵢ[σ₁₂] E₂.

Defined in

Mathlib.Analysis.Normed.Operator.LinearIsometry

Cited by

194 results in Mathlib

Foundations

Depth 11 from the axioms, rests on 91 definitions · uses no axioms

Assumes

SemiringSemiringSeminormedAddCommGroupSeminormedAddCommGroupModuleModule