Theorems · Theorem · functional analysis
ContinuousLinearMap.isStarProjection_iff_isIdempotentElem_and_isStarNormal
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : RCLike 𝕜] [inst_1 : NormedAddCommGroup E] [inst_2 : InnerProductSpace 𝕜 E]
{T : E →L[𝕜] E} [inst_3 : CompleteSpace E], IsStarProjection T ↔ IsIdempotentElem T ∧ IsStarNormal TA continuous linear map is a star projection iff it is idempotent and normal.
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- Foundations
- Depth 198 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- RingHom.idstatement and proof · cited by 18,349
- NormedAddCommGroupstatement and proof · cited by 15,752
- ContinuousLinearMapstatement and proof · cited by 5,352
- InnerProductSpacestatement and proof · cited by 3,523
- RCLikestatement and proof · cited by 2,829
- CompleteSpacestatement and proof · cited by 2,532
- IsIdempotentElemstatement and proof · cited by 217
- IsStarNormalstatement and proof · cited by 117
- IsStarProjectionstatement · cited by 64
- isStarProjection_iffproof · cited by 6
- ContinuousLinearMap.IsIdempotentElem.isSelfAdjoint_iff_isStarNormalproof · cited by 2
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