Theorems · Definition · operator theory

compactOperator

{R₁ : Type u_1} →
  {R₄ : Type u_2} →
    [inst : Semiring R₁] →
      [inst_1 : CommSemiring R₄] →
        (σ₁₄ : R₁ →+* R₄) →
          (M₁ : Type u_3) →
            (M₄ : Type u_5) →
              [inst_2 : TopologicalSpace M₁] →
                [inst_3 : AddCommMonoid M₁] →
                  [inst_4 : TopologicalSpace M₄] →
                    [inst_5 : AddCommGroup M₄] →
                      [inst_6 : Module R₁ M₁] →
                        [inst_7 : Module R₄ M₄] →
                          [inst_8 : ContinuousConstSMul R₄ M₄] →
                            [inst_9 : IsTopologicalAddGroup M₄] → Submodule R₄ (M₁ →SL[σ₁₄] M₄)

The submodule of compact continuous linear maps.

Defined in

Mathlib.Analysis.Normed.Operator.Compact.Basic

Cited by

2 results in Mathlib

Foundations

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

Assumes

SemiringCommSemiringTopologicalSpaceAddCommMonoidTopologicalSpaceAddCommGroupModuleModuleContinuousConstSMulIsTopologicalAddGroup