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Bilinear matrix inequalities and polynomials in several freely noncommuting variables
Sriram Balasubramanian, Neha Hotwani, Scott McCullough
Matrix-valued polynomials in any finite number of freely noncommuting variables that enjoy certain canonical partial convexity properties are characterized, via an algebraic certif…
Szego and Widom Theorems for the Neil Algebra
Sriram Balasubramanian, Scott McCullough, Udeni Wijesooriya
Versions of well known function theoretic operator theory results of Szego and Widom are established for the Neil algebra. The Neil algebra is the subalgebra of the algebra of boun…
Compact Sets in the Free Topology
Meric Augat, Sriram Balasubramanian, Scott McCullough
Subsets of the set of -tuples of matrices that are closed with respect to direct sums and compact in the free topology are characterized. They are, in a dilation theoretic sense…
Toeplitz Corona and the Douglas Property for Free Functions
Sriram Balasubramanian
The well known Douglas Lemma says that for operators on Hilbert space that implies for some contraction operator . The result carries over dire…
An Extended Reich Fixed Point Theorem
Sriram Balasubramanian
We obtain an extended Reich fixed point theorem for the setting of generalized cone rectangular metric spaces without assuming the normality of the underlying cone. Our work is a g…
Quasi-Convex Free Polynomials
Sriram Balasubramanian, Scott McCullough
Let $\Rx$ denote the ring of polynomials in freely non-commuting variables . There is a natural involution * on $\Rx$ determined by and $(pq)^*=q^*…
Non-commutative Caratheodory Interpolation
Sriram Balasubramanian
We prove a Caratheodory-Fejer type interpolation theorem for certain matrix convex sets in $\C^d$ using the Blecher-Ruan-Sinclair characterization of abstract operator algebras. Ou…