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Globally trace-positive noncommutative polynomials and the unbounded tracial moment problem
A noncommutative (nc ) polynomial is called (globally) trace-positive if its evaluation at any tuple of operators in a tracial von Neumann algebra...
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Quasidiagonality and tracial approximation
This chapter is somewhat different from the previous three chapters. Instead of constructing C*-algebras which we then show are simple (or find...
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States and Representations
A positive linear functional on a C∗-algebra is one that takes positive elements to non-negative numbers. They are automatically bounded, and among...
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Hereditary uniform property Γ
We study the uniform property Γ for separable simple C *-algebras which have quasitraces and may not be exact. We show that a stably finite separable...
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Tracial States and Representations of C∗-algebras
In this chapter we adapt a technique, borrowed from the theory of II1 factors, of juxtaposing the GNS Hilbert space structure associated with a...
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Stability of Rotation Relations of Three Unitaries with the Flip Action in C*-Algebras
The authors show that if Θ = ( θ jk ) is a 3 × 3 totally irrational real skew-symmetric matrix, where θ jk ∈ [0, 1) for j, k = 1, 2, 3, then for any ε >...
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Characterizing Jordan homomorphisms
It is shown that every bounded, unital linear map** that preserves elements of square zero from a C *-algebra of real rank zero and without tracial...
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Regularity Properties of Certain Crossed Product C*-Algebras
We show that the following properties of C* -algebras in a class Ω are inherited by simple unital C*-algebras in class TAΩ: (1) m -comparison of...
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State polynomials: positivity, optimization and nonlinear Bell inequalities
This paper introduces state polynomials, i.e., polynomials in noncommuting variables and formal states of their products. A state analog of Artin’s...
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A note on commutator-simple algebras
We investigate the property of commutator-simplicity in algebras from both algebraic and analytic perspectives. We demonstrate that a large class of...
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Hermitian geometry on the resolvent set (II)
For an element A in a unital C *-algebra ℬ , the operator-valued 1-form ω a ( z ) = ( z − A ) −1 dz is analytic on the resolvent set ρ ( A ), which plays an...
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Exactness Versus C*-Exactness for Certain Non-discrete Groups
It is known that exactness for a discrete group is equivalent to C*-exactness, i.e., the exactness of its reduced C*-algebra. The problem of whether...
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Five Hilbert Space Problems in Operator Algebras
A number of questions which have been solved over the years in the theory of single operators acting on Hilbert space have interesting analogues when...