Some Permanence for crossed products by compact group actions with the tracial Rokhlin property

The paper discusses some properties of the crossed product and the fixed point algebra of a unital simple separable infinite dimensional $C^*$-algebra by an acton of a second countable compact group with the tracial Rokhlin property with comparison that could be deduced from the properties of its origin algebra. (1) stable rank one; (2) real rank zero; (3) $\beta$-comparison; (4) $n$-comparison; (5) $m$-almost divisible; (6) weakly ($m$,$n$)-divisible.
Comment: arXiv admin note: substantial text overlap with arXiv:2110.12135 by other authors