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Theorems · Theorem · operator theory

IsCompactOperator.smul_iff

∀ {M₁ : Type u_3} {M₂ : Type u_4} [inst : TopologicalSpace M₁] [inst_1 : AddCommMonoid M₁]
  [inst_2 : TopologicalSpace M₂] [inst_3 : AddCommMonoid M₂] {S : Type u_6} [inst_4 : Group S]
  [inst_5 : DistribMulAction S M₂] [ContinuousConstSMul S M₂] {f : M₁ → M₂} (c : S),
  IsCompactOperator (c • f) ↔ IsCompactOperator f
Defined in
Mathlib.Analysis.Normed.Operator.Compact.Basic
Cited by
0 results in Mathlib
Foundations
Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
TopologicalSpaceAddCommMonoidTopologicalSpaceAddCommMonoidGroupDistribMulActionContinuousConstSMul
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TopologicalSpace · cited by 24529TopologicalSpaceAddCommMonoid · cited by 12281AddCommMonoidGroup · cited by 6238GroupContinuousConstSMul · cited by 832ContinuousConstSMulDistribMulAction · cited by 584DistribMulActionIsCompactOperator · cited by 51IsCompactOperatorGroup.isUnit · cited by 18Group.isUnitIsCompactOperator.smul_isUnit_iff · cited by 2IsCompactOperator.smul_is…IsCompactOperator.smul_iffCITED BYCITES

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