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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…
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…
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…