The inheritance tracial topological rank zero for centrally large subalgebra

Abstract

Let $A$ be an infinite-dimensional unital simple C*-algebra such that A has $\mu$-$oz\mathrm{LLP}$ property for any $\mu \in (0,1)$. Let $B\subseteq A$ be a centrally large subalgebra of $A$ such that $B$ has tracial topological rank zero. Then $A$ has tracial topological rank zero.

arXiv commentarXiv admin note: substantial text overlap with arXiv:2309.08900, arXiv:2203.05700, arXiv:2310.12548, arXiv:2310.04718, arXiv:2206.05036