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Saikat Mahapatra

Publications and source records attributed to Saikat Mahapatra.

6 recordsLinked to original sources
arXiv2026

$q$-Berezin sectorial operators with applications to $q$-Berezin number inequalities and $q$-Berezin ranges

In this paper, we introduce a new class of operators, called $q$-Berezin sectorial operators, as an extension of the class of $q$-sectorial operators. By presenting examples on the Hardy-Hilbert space, we show that there exist operators which are $q$-Berezin sectorial but not $q$-sectorial. Several new inequalities for the $q$-Berezin number associated with this class of operators are also derived. In addition, we investigate the geometric structure of the $q$-Berezin range for various classes of operators on the Bergman space, including weighted shift and certain composition operators.

math.FA↗
arXiv2026

Improved upper bounds for the Berezin numbers of operators on reproducing kernel Hilbert spaces

In this article, several upper bounds for the Berezin numbers of bounded linear operators on reproducing kernel Hilbert spaces are obtained through the use of interpolation paths of symmetric means and Orlicz functions. With suitable selections of these paths and functions, we show that the results presented here refine and generalize several earlier known findings. Furthermore, we derive some Berezin number inequalities for such operators using refined Young's inequalities.

math.FA↗
arXiv2026

Improved Bounds for numerical radius and $a$-numerical radius in ${C}^*$-algebras

In this article, we derive several significant upper bounds for the numerical radius and $a$-numerical radius of an element in a ${C}^*$-algebra by improving inequalities for positive linear functionals. Our findings refine and generalize the existing inequalities. Furthermore, we introduce a new notion to derive improved upper bounds of the numerical radius for an element in a ${C}^*$-algebra using the Moore-Penrose inverse.

math.FA↗
arXiv2026

An introduction of Berezin sectorial operators and its application to Berezin number inequalities

We introduce a new class of operators, called Berezin sectorial operators, which generalizes classical sectorial operators. We provide examples on the Hardy-Hilbert space showing that there exist operators that are Berezin sectorial but not sectorial and that the Berezin sectorial index can be strictly smaller than the classical one. We derive Berezin number inequalities for this class, including a weak version of the power inequality, and study geometric properties of the Berezin range for finite-rank and weighted shift operators on the Dirichlet space. We also raise the question of whether similar constructions are possible for composition-differentiation operators on the Dirichlet space.

math.FA↗