1 citations · 1 across the 4 of their papers we have counts for
7 papers
Singular inner eigenfunctions of composition operators
V. A. Anjali, P. Muthukumar, P. Shankar
This paper characterizes all the singular inner eigenfunctions of the composition operators that arise from discrete measures, when is an automorphism of unit disk. By es…
On the convexity of Berezin range and Berezin radius inequalities via a class of semi-norms
Athul Augustine, P. Hiran Das, Pintu Bhunia +1
This paper introduces a new family of semi-norms, say -Berezin norm on the space of all bounded linear operators defined on a reproducing kernel Hilbert space…
A Family of Semi-norms in -algebras
Athul Augustine, Pintu Bhunia, P. Shankar
We introduce a new family of non-negative real-valued functions on a -algebra , i.e., for $$\|a\|_{σ_μ}= \text{sup}\left\lbrace \sqrt{|f(a)|^2 σ_…
Convexity of the Berezin range of finite rank operators
Athul Augustine, M. Garayev, P. Shankar
For a bounded linear operator acting on a reproducing kernel Hilbert space over a nonempty set , the Berezin range of is defined by \[ \mathrm{Ber}(T)=\…
Composition operators between Beurling subspaces of Hardy space
V. A. Anjali, P. Muthukumar, P. Shankar
V. Matache (J. Operator Theory 73(1):243--264, 2015) raised an open problem about characterizing composition operators on the Hardy space and nonzero singular measures…
On the convexity of the Berezin range of composition operators and related questions
Athul Augustine, M. Garayev, P. Shankar
The Berezin range of a bounded operator acting on a reproducing kernel Hilbert space is the set := $\{\langle T\hat{k}_{x},\hat{k}_{x} \rangle_{\mathcal{H}…
Isometric pairs with compact and normal cross-commutator
Sandipan De, Jaydeb Sarkar, P Shankar +1
We represent and classify pairs of commuting isometries acting on Hilbert spaces that satisfy the condition \[ [V_1^*, V_2] = \text{compact and normal}, \] where $[V_1…