7 papers · 1 filter
Constrained dilation and -contractions
Sourav Pal, Nitin Tomar
A commuting pair of Hilbert space operators having the closed symmetrized bidisc \[ Γ=\{(z_1+z_2, z_1z_2) \in \mathbb C^2 \ : \ |z_1| \leq 1, |z_2| \leq 1\} \] as a spectral set is…
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…
Spectral set, complete spectral set and dilation for Banach space operators
Swapan Jana, Sourav Pal
Famous results due to von Neumann, Sz.-Nagy and Arveson assert that the following four statements are equivalent; a Hilbert space operator is a contraction; the closed unit dis…
Classification and dilation for -commuting scalar matrices
Sourav Pal, Prajakta Sahasrabuddhe, Nitin Tomar
A tuple of operators on a Hilbert space is said to be \textit{-commuting with} or simply -\textit{commuting} if ther…
Lifting -commuting and -intertwining operators
Sourav Pal, Prajakta Sahasrabuddhe
There are several proofs of the classical commutant lifting and intertwining lifting theorems in the literature. In this article, we present analogous proofs to a few -commuting…
Triangular Tetrablock-contractions, factorization of contractions, dilation and subvarieties
Sourav Pal
A commuting triple of Hilbert space operators , for which the closed tetrablock is a spectral set, is called a \textit{tetrablock-contraction} or simply…