arXiv subjects

Soumyadip Dey

Publications and source records attributed to Soumyadip Dey.

2 recordsLinked to original sources

arXiv2026

Cauchy Dual Subnormality for Toral 2-Isometric Operator-Valued 2-Variable Weighted Shift

In this paper, we show that if $\mathbf{T} = (T_1, T_2)$ is an analytic left-inverse commuting pair of toral $2$-isometries satisfying the joint kernel condition, then it is unitarily equivalent to an operator-valued weighted shift with invertible weights $\{W_{I}^{(j)}:j=1,2\}_{I\in \mathbb{Z}_{+}^2},$ where the initial weights $W_{0,0}^{(1)}$ and $W_{0,0}^{(2)}$ are positive operators. Moreover, if these initial weights commute, then the Cauchy dual $\mathbf{T}' := (T_1', T_2')$ is jointly subnormal. We also construct an example in which the initial weights do not commute, and the corresponding Cauchy dual fails to be jointly subnormal.

math.FA↗

arXiv2026

von Neumann Inequality for a class of Doubly Contractive Weighted Shifts

In this article, we investigate the ball version of von Neumann inequality for the class of doubly contractive $d$-tuple of weighted shift. We show that if the weighted shift is balanced or satisfies an appropriate weight condition, then it admits a spherical unitary dilation. Consequently, such tuples satisfy the von Neumann inequality over Euclidean unit ball. For the general class of commuting tuple of doubly contractive operators (not necessarily weighted shift) on a Hilbert space, we further establish von Neumann inequality for homogeneous polynomials of degree at most $2.$

math.FA↗