Autor-Archive: hannesthiel

Purely infinite rings and C*-algebras

Von | September 23, 2020

Question 1: If is a *-subalgebra of bounded linear operators on a separable Hilbert space such that is purely infinite as a ring, is the norm-closure purely infinite as a C*-algebra? This is Problem 8.4 in ​[1]​. As noted in Problem 8.6 in ​[1]​, this is even unclear if is a unital, simple, purely infinite… Weiterlesen »

Liftable normal elements

Von | September 22, 2020

Given a C*-algebra and a closed, two-sided ideal , is the image of the normal elements in under the quotient map a closed subset of ? Equivalently, if is a sequence of normal elements in that converge to , and if each admits a normal lift in , does admit a normal lift? This question… Weiterlesen »

Simple, Z-stable, projectionless C*-algebras

Von | September 22, 2020

Do simple, -stable, stably projectionless C*-algebras have stable rank one? Definitions: A C*-algebra is said to be -stable if it tensorially absorbs the Jiang-Su algebra , that is, . Further, a simple C*-algebra is projectionless if it contains no nonzero projections, and it is stably projectionless if is projectionless. (In the nonsimple case, one should… Weiterlesen »

Nonregular, simple, nuclear C*-algebras

Von | September 7, 2020

(Based on the talk „Thoughts on the classification problem for amenable C*-algebras“ of George Elliott, 30. June 2020, at the Zagreb Workshop on Operator Theory.) Let us consider the class of unital, separable, simple, nuclear C*-algebras. The Toms-Winter conjecture predicts that for such an algebra , the following conditions are equivalent: has finite nuclear dimension.… Weiterlesen »

Real rank of B(H) tensor B(H)

Von | Juni 20, 2020

Given a separable, infinite-dimensional Hilbert space , what is the real rank of the minimal tensor product ? Background/Motivation: The real rank is a noncommutative dimension theory that was introduced by Brown and Pedersen in ​[1]​. It associates to each C*-algebra a number (its real rank) . The lowest and most interesting value is zero.… Weiterlesen »

Automorphisms of the Calkin algebra

Von | Juni 20, 2020

Does the Calkin algebra admit an automorphism that induces the flip on ? Background/Motivation: Let be a separable, infinite-dimensional Hilbert space. The Calkin algebra is the quotient of the bounded, linear operators on by the closed, two-sided ideal of compact operators. The important problem of whether the Calkin algebra has outer automorphisms was eventually shown… Weiterlesen »