This is one of the few problems from the Scottish book that are still open. In modern terminology, the problem is: Let and be Banach spaces, and let be a bijective map with the following property: For every there exists such that for the sphere , the restriction is isometric. Does it follow that is… Weiterlesen »
Given groups and , let us say that the pair has property (*) if any two injective homomorphisms are conjugate if (and only if) they are pointwise conjugate. Problem 1: Describe the class of groups such that has (*) for every group . Problem 2: Describe the class of groups such that has (*) for… Weiterlesen »
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 »
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 »
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 »
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 »
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