27 citations · 34 across the 12 of their papers we have counts for
15 papers
Circular operators and their strong circularity
Soumitra Ghara, Surjit Kumar, Shailesh Trivedi
Circular operators have been studied extensively since the work of R. Gellar, who conjectured that every circular operator on a complex separable Hilbert space is strongly circular…
Weakly -homogeneous commuting tuple of bounded operators
Soumitra Ghara, Surjit Kumar, Shailesh Trivedi
We introduce and study the weakly -homogeneous commuting tuple of operators. We provide a sufficient condition under which a weakly -homogeneous tuple…
Unitary equivalence of balanced weighted shifts on rooted directed trees
Shubhankar Mandal, Shailesh Trivedi
We completely characterize non-periodic balanced weighted shifts $S_{\lambdab}$ on rooted directed trees under a very mild assumption that $S_{\lambdab}^{*n}S_{\lambdab}^n|_{\ker S…
Wold-type decomposition for left-invertible weighted shifts on a rootless directed tree
Sameer Chavan, Shailesh Trivedi
Let $S_{\lambdab}$ be a bounded left-invertible weighted shift on a rootless directed tree We address the question of when $S_{\lambdab}$ has Wold-typ…
A short note on similarity of operator-valued multishifts
Soumitra Ghara, Surjit Kumar, Shailesh Trivedi
A complete characterization of the similarity between two operator-valued multishifts with invertible operator weights is obtained purely in terms of operator weights. This general…
Failure of the wandering subspace property for analytic norm-increasing -isometries
Sameer Chavan, Shailesh Trivedi
We construct an analytic norm-increasing -isometric weighted shift on a rootless directed tree, which does not have the wandering subspace property. This answers a question of S…
Bounded point evaluation for operators with the wandering subspace property
Shailesh Trivedi
We extend and study the notion of bounded point evaluation introduced by Williams for a cyclic operator to the class of operators with the wandering subspace property. We character…
Unitary equivalence of operator-valued multishifts
Rajeev Gupta, Surjit Kumar, Shailesh Trivedi
We systematically study various aspects of operator-valued multishifts. Beginning with basic properties, we show that the class of multishifts on the directed Cartesian product of…
Analytic -isometries without the wandering subspace property
Akash Anand, Sameer Chavan, Shailesh Trivedi
The wandering subspace problem for an analytic norm-increasing -isometry on a Hilbert space asks whether every -invariant subspace of can be gen…
Von Neumann's inequality for commuting operator-valued multishifts
Rajeev Gupta, Surjit Kumar, Shailesh Trivedi
Recently, Hartz proved that every commuting contractive classical multishift with non-zero weights satisfies the matrix-version of von Neumann's inequality. We show that this resul…
Commutants and Reflexivity of Multiplication tuples on Vector-valued Reproducing Kernel Hilbert Spaces
Sameer Chavan, Shubhankar Podder, Shailesh Trivedi
Motivated by the theory of weighted shifts on directed trees and its multivariable counterpart, we address the question of identifying commutant and reflexivity of the multiplicati…
Classification of Drury-Arveson-type Hilbert modules associated with certain directed graphs
Sameer Chavan, Deepak Kumar Pradhan, Shailesh Trivedi
Given a directed Cartesian product of locally finite, leafless, rooted directed trees of finite joint branching index, one may ass…
Dirichlet Spaces Associated With Locally Finite Rooted Directed Trees
Sameer Chavan, Deepak Kumar Pradhan, Shailesh Trivedi
Let be a leafless, locally finite rooted directed tree. We associate with a one parameter family of Dirichlet spaces $\mathscr H_q~(q \geq…
Multishifts on Directed Cartesian Product of Rooted Directed Trees
Sameer Chavan, Deepak Kumar Pradhan, Shailesh Trivedi
We systematically develop the multivariable counterpart of the theory of weighted shifts on rooted directed trees. Capitalizing on the theory of product of directed graphs, we intr…
An Analytic Model for Left-Invertible Weighted Shifts on Directed Trees
Sameer Chavan, Shailesh Trivedi
Let be a rooted directed tree with finite branching index and let be a left-invertible weighted shift on . We show t…