The (matricial) solution set of a Linear Matrix Inequality (LMI) is a convex non-commutative basic open semi-algebraic set (defined below). The main theorem of this paper is a converse, a resultâ€¦ (More)

In this paper, we analyze problems involving matrix variables for which we use a noncommutative algebra setting. To be more specific, we use a class of functions (called NC analytic functions)â€¦ (More)

Agler's abstract model theory is applied to C, the family of operators with unitary-dilations, where is a xed number in (0; 2]. The extremals, which are the collection of operators in C with theâ€¦ (More)

In communications and signal processing, we can find examples of applications that could benefit from the prediction of a bandlimited random process. We consider a continuous-time linear predictorâ€¦ (More)

Let R denote a domain in C with boundary B. Let X denote the closure of R. An operator T on a complex Hilbert space H has X as a spectral set if Ïƒ(T ) âŠ‚ X and â€–f(T )â€– â‰¤ â€–fâ€–R = sup{|f(z)| : z âˆˆ R} forâ€¦ (More)

This paper concerns the geometry of noncommutative domains and analytic free maps. These maps are free analogs of classical analytic functions in several complex variables, and are defined in termsâ€¦ (More)

We study, in the spirit of modern real algebra, the interplay between left ideals of the free âˆ—-algebra F with n generators, and their suitably defined zero sets; and similarly between quadraticâ€¦ (More)

This research examined the sustainability of Canada's At Home/Chez Soi Housing First (HF) programs for homeless persons with mental illness 2Â years after the end of the demonstration phase of a largeâ€¦ (More)

The (matrical) solution set of a Linear Matrix Inequality (LMI) is a convex basic non-commutative semi-algebraic set (defined below). The main theorem of this paper is a converse, a result which hasâ€¦ (More)