Every finite dimensional $C^*$ algebra can be decomposed into the finite direct sum of the form $M_n(\mathbb{C})$.I guess that every infinite nuclear $C^*$ algebra can be decomposed into $c_0$ sum of the form $M_n(\mathbb{C})$.Is that true?If it is true,how to prove it?
2026-03-25 11:19:17.1774437557
Decomposition of infinite nuclear $C^*$ algebra
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The answer is no. Even Abelian $C^\ast$-algebras fail that if their spectrum is not discrete.