4 papers
Spectra of -Contractions via Characteristic Functions
Abhay Jindal, Poornendu Kumar
A unitarily invariant complete Nevanlinna--Pick (CNP) kernel on the Euclidean ball gives rise to a natural class of operator tuples on Hilbert spaces, known as -contractio…
Pure UCP Maps on Finite Toeplitz Systems and Quantum Gromov--Hausdorff Convergence
Ritul Duhan, Abhay Jindal
We study pure unital completely positive maps on the finite Toeplitz operator system of Toeplitz matrices. Our first main result gives an explicit characteriz…
Operator-Valued Positivstellensätze on Matrix Convex Sets and Free Products of Finite Abelian Groups
Abhay Jindal, Igor Klep, Scott McCullough
We prove a Positivstellensatz for operator-valued noncommutative polynomials that are positive on matrix convex sets. Specifically, let be an operator-valued polynomial in $B(H…
Positive operator-valued noncommutative polynomials are squares
Abhay Jindal, Igor Klep, Scott McCullough
We establish operator-valued versions of the earlier foundational factorization results for noncommutative polynomials due to Helton (Ann.~Math., 2002) and one of the authors (Line…