7 papers · 1 filter
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…
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…
Operator Theory on the Pentablock
Abhay Jindal, Poornendu Kumar
The pentablock, denoted as $\cP,$ is defined as follows: $$\cP= \left\{ (a_{21}, {\rm tr}(A), {\rm det}(A)) : A = [a_{ij}]_{2 \times 2} \text{ with } \|A\|<1 \right\}.$$ It origina…
Complete Nevanlinna-Pick Kernels and the Curvature Invariant
Tirthankar Bhattacharyya, Abhay Jindal
We consider a unitarily invariant complete Nevanlinna-Pick kernel denoted by and a commuting -tuple of bounded operators satisfying a natural con…
Complete Nevanlinna-Pick kernels, the Schwarz lemma and the Schur algorithm
Daniel Alpay, Tirthankar Bhattacharyya, Abhay Jindal +1
We investigate the Schwarz lemma and the Schur algorithm for elements in the unit ball of the multiplier algebra of a reproducing kernel Hilbert space on the open unit ball whose k…