Nik Weaver

The Calkin algebra has outer automorphisms

Assuming the continuum hypothesis, we show that the Calkin algebra has 2^{aleph_1} outer automorphisms.

A prime C∗-algebra that is not primitive

We construct a nonseparable C∗-algebra that is prime but not primitive. This solves an old problem of Dixmier.

On the universality of almost every quantum logic gate

Lloyd [Phys. Rev. Lett. 75, 346 (1995)] showed that almost every quantum logic gate is universal in the sense that it can be used to approximate any unitary transformation. The argument relied on a more general fact whose proof was not given in detail. We give a complete proof of this more general fact.

Geometric characterizations of some classes of operators in C*-algebras and von Neumann algebras

We present geometric characterizations of the partial isometries, unitaries, and invertible operators in C*-algebras and von Neumann algebras.

A Lyapunov‐type theorem from Kadison–Singer

Marcus, Spielman, and Srivastava recently solved the Kadison-Singer problem by showing that if u_1, ..., u_m are column vectors in C^d such that \sum u_iu_i^* = I, then a set of indices S \subseteq {1, ..., m} can be chosen so that \sum_{i \in S} u_iu_i^* is approximately (1/2)I, with the approximation good in operator norm to order \epsilon^{1/2} where \epsilon = \max \|u_i\|^2. We extend their result to show that every linear combination of the matrices u_iu_i^* with coefficients in [0,1] can be approximated in operator norm to order \epsilon^{1/8} by a matrix of the form \sum_{i \in S} u_iu_i^*.

B(H) has a pure state that is not multiplicative on any masa.

Assuming the continuum hypothesis, we prove that ℬ(H) has a pure state whose restriction to any masa is not pure. This resolves negatively old conjectures of Kadison and Singer and of Anderson.

Time-optimal control of finite quantum systems

We investigate time-optimal control of finite quantum systems in the Born approximation. A bang–bang principle is found to follow from a result in [C. A. Akemann and J. Anderson, Mem. Amer. Math. Soc. 458 (1991)]. We also prove existence of time-optimal controls, characterize when they are unique, and assuming uniqueness, explicitly describe them.

PURE STATES ON FREE GROUP C*-ALGEBRAS

We prove that all of the pure states of the reduced C*-algebra of the free goup on

Lipschitz Algebras and Derivations II. Exterior Differentiation

\aleph_1

Consistency of a counterexample to Naimark's problem

generators are *-automorphism equivalent and extract some consequences of that fact.