instNonUnitalCStarAlgebra — Mathlib

English

Matrices with entries in a nonunital C*-algebra A form a NonUnitalCStarAlgebra (duplicate statement).

Русский

Матрицы с элементами ненулевой C*-алгебры A повторно образуют ненулевую C*-алгебру.

LaTeX

$$$$\\mathrm{NonUnitalCStarAlgebra}(\\mathrm{CStarMatrix}(n,n,A)).$$$$

Lean4

/-- Matrices with entries in a non-unital C⋆-algebra form a non-unital C⋆-algebra. -/
noncomputable instance instNonUnitalCStarAlgebra : NonUnitalCStarAlgebra (CStarMatrix n n A)
    where
  smul_assoc x y z := by simp
  smul_comm m a b := (Matrix.mul_smul _ _ _).symm

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