arXiv subjects

Anirban Sen

Publications and source records attributed to Anirban Sen.

23 records · Page 2Linked to original sources

arXiv2022

Davis-Wielandt-Berezin radius inequalities of Reproducing kernel Hilbert space operators

Several upper and lower bounds of the Davis-Wielandt-Berezin radius of bounded linear operators defined on a reproducing kernel Hilbert space are given. Further, an inequality involving the Berezin number and the Davis-Wielandt-Berezin radius for the sum of two bounded linear operators is obtained, namely, if $A $ and $B$ are reproducing kernel Hilbert space operators, then $$η(A+B) \leq η(A)+η(B)+\textbf{ber}(A^*B+B^*A),$$ where $η(\cdot)$ and $\textbf{ber}(\cdot)$ are the Davis-Wielandt-Berezin radius and the Berezin number, respectively.

math.FA↗

arXiv2022

Development of the Berezin number inequalities

We present new bounds for the Berezin number inequalities which improve on the existing bounds. We also obtain bounds for the Berezin norm of operators as well as the sum of two operators.

math.FA↗

arXiv2021

Inequalities involving Berezin norm and Berezin number

We obtain new inequalities involving Berezin norm and Berezin number of bounded linear operators defined on a reproducing kernel Hilbert space $\mathscr{H}.$ Among many inequalities obtained here, it is shown that if $A$ is a positive bounded linear operator on $\mathscr{H}$, then $\|A\|_{ber}=\textbf{ber}(A)$, where $\|A\|_{ber}$ and $\textbf{ber}(A)$ are the Berezin norm and Berezin number of $A$, respectively. In contrast to the numerical radius, this equality does not hold for selfadjoint operators, which highlights the necessity of studying Berezin number inequalities independently.

math.FA↗

arXiv2021

New semi-norm of semi-Hilbertian space operators and its application

In this paper, we introduce a new semi-norm of operators on a semi-Hilbertian space, which generalizes the A-numerical radius and A-operator semi-norm. We study the basic properties of this semi-norm, including upper and lower bounds for it. As an application of this new semi-norm, we obtain upper bounds for the A-numerical radius of semi-Hilbertian space operators, which are sharper than the earlier ones.

math.FA↗

arXiv2015

On the Role of Conductance, Geography and Topology in Predicting Hashtag Virality

We focus on three aspects of the early spread of a hashtag in order to predict whether it will go viral: the network properties of the subset of users tweeting the hashtag, its geographical properties, and, most importantly, its conductance-related properties. One of our significant contributions is to discover the critical role played by the conductance based features for the successful prediction of virality. More specifically, we show that the first derivative of the conductance gives an early indication of whether the hashtag is going to go viral or not. We present a detailed experimental evaluation of the effect of our various categories of features on the virality prediction task. When compared to the baselines and the state of the art techniques proposed in the literature our feature set is able to achieve significantly better accuracy on a large dataset of 7.7 million users and all their tweets over a period of month, as well as on existing datasets.

cs.SI↗