4 papers · 1 filter
On a minimal Andô dilation for a pair of strict contractions
Swapan Jana, Sourav Pal
The isometric dilation of a pair of commuting contractions due to Andô is not minimal. We modify Andô's dilation and construct a minimal isometric dilation on $\mathcal H \oplus_2…
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…
A dilation theoretic approach to Banach spaces
Swapan Jana, Sourav Pal, Saikat Roy
For a complex Banach space , we prove that is a Hilbert space if and only if every strict contraction on dilates to an isometry if and only i…
Remarks on positive definite functions on a group
Swapan Jana, Sourav Pal, Nitin Tomar
We study the operator-valued positive definite functions on a group using positive block matrices. We give an alternative proof to Brehmer positivity for doubly commuting contracti…