Schlagwort-Archive: C*-algebras

Introduction: The study of automatic continuity for homomorphisms (multiplicative, linear maps) between Banach algebras has a long history. In 1960, Bade and Curtis [1] proved the existence of discontinuous homomorphisms between commutative Banach algebras in ZFC, showing that automatic continuity results can only be achieved by imposing additional hypotheses on the algebras , or on… Weiterlesen »

Question: Is the minimal tensor product of two C*-algebras pure whenever one of them is? Background: Following Winter [1], a C*-algebra is said to be pure if it has very good comparison and divisibility properties, specifically its Cuntz semigroup is almost unperforated and almost divisible. This notion is closely related to that of -stability, where… Weiterlesen »

Given elements and in a ring, the element is called an (additive) commutator. Given a C*-algebra , we use to denote the additive subgroup (equivalently, the linear subspace) generated by the set of additive commutators in . Note that is not necessarily a closed subspace. Given additive subgroups and , it is customary to use… Weiterlesen »

It is known that every nuclear C*-algebra is exact, and that exactness passes to sub-C*-algebras. It follows that every sub-C*-algebra of a nuclear C*-algebra is exact. For separable C*-algebras, the converse holds. In fact, Kirchberg’s -embedding theorem shows that a separable C*-algebra is exact if and only if it embeds into the Cuntz algebra (which… Weiterlesen »

Does there exist a purely infinite C*-algebra that admits a tracial weight taking a finite, nonzero value? Here a C*-algebra is purely infinite if every element is properly infinite ( is Cuntz subequivalent to in ). This notion was introduced and studied by Kirchberg-Rørdam in ​[1]​ and ​[2]​. Further, a weight on a C*-algebra is… Weiterlesen »