Theorems · Theorem · functional analysis
IsStarNormal.commute_star_right
∀ {A : Type u_2} [inst : NonUnitalCStarAlgebra A] {a x : A}, IsStarNormal a → Commute x a → Commute x (star a)Fuglede–Putnam–Rosenblum: If a is a normal element in a C⋆-algebra A which
commutes with x, then star a commutes with x.
- Defined in
- Mathlib.Analysis.CStarAlgebra.Fuglede
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 293 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NonUnitalCStarAlgebra
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Star.starstatement · cited by 1,082
- Commutestatement and proof · cited by 639
- NonUnitalCStarAlgebrastatement and proof · cited by 149
- IsStarNormalstatement and proof · cited by 117
- SemiconjBy.star_rightproof · cited by 2
- Commute.semiconjByproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- IsStarNormal.norm_add_eq_maxproof · cited by 3
- IsStarNormal.commute_star_leftproof · cited by 1