14 papers · 1 filter
Operators associated with a domain in and applications
Sourav Pal, Nitin Tomar
The hexablock is a domain arising from a special case of the -synthesis problem. We study the commuting operator tuples having the hexablock as a spectral set. Such a tuple is…
Spectral constants for the quantum annulus
Sourav Pal, James E. Pascoe, Nitin Tomar
We find several new estimates for the spectral constants for which a closed annulus or closed polyannulus is a…
Theory of -commuting contractions-II: Regular dilation, Brehmer's positivity and von Neumann's inequality
Sourav Pal, Prajakta Sahasrabuddhe, Nitin Tomar
It is well-known that a commuting family of contractions possesses a regular unitary dilation if and only if it satisfies Brehmer's positivity condition. We extend this theorem to…
Operators associated with the pentablock and their relations with biball and symmetrized bidisc
Sourav Pal, Nitin Tomar
A commuting triple of Hilbert space operators is said to be a \textit{-contraction} if the closed pentablock is a spectral set for $(A,…
Constrained dilation and -contractions
Sourav Pal, Nitin Tomar
A commuting pair of Hilbert space operators having the closed symmetrized bidisc \[ Î=\{(z_1+z_2, z_1z_2) \in \mathbb C^2 \ : \ |z_1| \leq 1, |z_2| \leq 1\} \] as a spectral set i…
Dilation on an annulus and von Neumann's inequality on certain varieties in the biball
Sourav Pal, Nitin Tomar
We give an alternative proof to Agler's famous result on success of rational dilation on an annulus by an application of a result due to Dritschel and McCullough. We show interplay…