Theorems · Definition · functional analysis

ContinuousMultilinearMap.mkPiAlgebra

(R : Type u) →
  (ι : Type v) →
    (A : Type u_1) →
      [Fintype ι] →
        [inst : CommSemiring R] →
          [inst_1 : CommSemiring A] →
            [inst_2 : Algebra R A] →
              [inst_3 : TopologicalSpace A] → [ContinuousMul A] → ContinuousMultilinearMap R (fun x => A) A

The continuous multilinear map on A^ι, where A is a normed commutative algebra over 𝕜, associating to m the product of all the m i. See also ContinuousMultilinearMap.mkPiAlgebraFin.

Defined in

Mathlib.Topology.Algebra.Module.Multilinear.Basic

Cited by

13 results in Mathlib

Foundations

Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FintypeCommSemiringCommSemiringAlgebraTopologicalSpaceContinuousMul