instNonUnitalNormedRing — Mathlib

English

CStarMatrix(n,n,A) forms a NonUnitalNormedRing when A is a nonunital C*-algebra, with the matrix operations and the induced norm.

Русский

Матрицы CStarMatrix(n,n,A) образуют ненулевое нормированное кольцо (NonUnitalNormedRing) при A — ненулевая C*-алгебра, с операциями матричными и индуцированной нормой.

LaTeX

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

Lean4

noncomputable instance instNonUnitalNormedRing : NonUnitalNormedRing (CStarMatrix n n A)
    where
  __ : NormedAddCommGroup (CStarMatrix n n A) := inferInstance
  __ : NonUnitalRing (CStarMatrix n n A) := inferInstance
  norm_mul_le _ _ := by simpa only [norm_def', map_mul] using norm_mul_le _ _

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