4 papers
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)…
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 spa…
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…
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\|_{Ï_μ}= \text{sup}\left\lbrace \sqrt{|f(a)|^2…