Theorems · Definition · functional analysis

LinearIsometryClass

(𝓕 : Type u_11) →
  (R : outParam (Type u_12)) →
    (E : outParam (Type u_13)) →
      (E₂ : outParam (Type u_14)) →
        [inst : Semiring R] →
          [inst_1 : SeminormedAddCommGroup E] →
            [inst_2 : SeminormedAddCommGroup E₂] → [Module R E] → [Module R E₂] → [FunLike 𝓕 E E₂] → Prop

LinearIsometryClass F R E E₂ asserts F is a type of bundled R-linear isometries M → M₂. This is an abbreviation for SemilinearIsometryClass F (RingHom.id R) E E₂.

Defined in: Mathlib.Analysis.Normed.Operator.LinearIsometry
Cited by: 0 results in Mathlib
Foundations: Depth 13 from the axioms · uses no axioms
Assumes: Semiring SeminormedAddCommGroup SeminormedAddCommGroup Module Module FunLike

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Modulestatement and proof · cited by 20,661
RingHom.idproof · cited by 18,349
Semiringstatement and proof · cited by 13,802
SeminormedAddCommGroupstatement and proof · cited by 2,671
FunLikestatement and proof · cited by 2,560
SemilinearIsometryClassproof · cited by 11

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