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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…