A Direct Proof of Z-stability for Ah Algebras of Bounded Topological Dimension
نویسندگان
چکیده
We prove that a unital simple approximately homogeneous (AH) C-algebra with no dimension growth absorbs the Jiang-Su algebra tensorially without appealing to the classification theory of these algebras. Our main result continues to hold under the slightly weaker hypothesis of exponentially slow dimension growth.
منابع مشابه
A direct proof of Z-stability for approximately homogeneous C∗-algebras of bounded topological dimension
We prove that a unital simple approximately homogeneous C*-algebra with no dimension growth absorbs the Jiang–Su algebra tensorially without appealing to the classification theory of these algebras. Our main result continues to hold under the slightly weaker hypothesis of exponentially slow dimension growth.
متن کاملClassifying C*-algebras via ordered, mod-p K-theory
We introduce an order structure on K 0 ( ) 9 K0(; Z/p ) . This group may also be thought of as Ko(; 7z @ Z/p ) . We exhibit new examples of real-rank zero C*-algebras that are inductive limits of finite dimensional and dimension-drop algebras, have the same ordered, graded K-theory with order unit and yet are not isomorphic. In fact they are not even stably shape equivalent. The order structure...
متن کاملThe Elliott Conjecture for Villadsen Algebras of the First Type
We study the class of simple C-algebras introduced by Villadsen in his pioneering work on perforated ordered K-theory. We establish six equivalent characterisations of the proper subclass which satisfies the strong form of Elliott’s classification conjecture: two C-algebraic (Z-stability and approximate divisibility), one K-theoretic (strict comparison of positive elements), and three topologic...
متن کاملStrong Topological Regularity and Weak Regularity of Banach Algebras
In this article we study two different generalizations of von Neumann regularity, namely strong topological regularity and weak regularity, in the Banach algebra context. We show that both are hereditary properties and under certain assumptions, weak regularity implies strong topological regularity. Then we consider strong topological regularity of certain concrete algebras. Moreover we obtain ...
متن کاملApproximate solutions of homomorphisms and derivations of the generalized Cauchy-Jensen functional equation in $C^*$-ternary algebras
In this paper, we prove Hyers-Ulam-Rassias stability of $C^*$-ternary algebra homomorphism for the following generalized Cauchy-Jensen equation $$eta mu fleft(frac{x+y}{eta}+zright) = f(mu x) + f(mu y) +eta f(mu z)$$ for all $mu in mathbb{S}:= { lambda in mathbb{C} : |lambda | =1}$ and for any fixed positive integer $eta geq 2$ on $C^*$-ternary algebras by using fixed poind alternat...
متن کامل