4 papers
Spectra of -Contractions via Characteristic Functions
Abhay Jindal, Poornendu Kumar
A unitarily invariant complete Nevanlinna--Pick (CNP) kernel on the Euclidean ball gives rise to a natural class of operator tuples on Hilbert spaces, known as -contractio…
Multiplicative linear functionals on reproducing kernel Hilbert spaces
Tirthankar Bhattacharyya, Jaikishan, Poornendu Kumar +1
The classical Gleason--Kahane--Zelazko theorem characterizes multiplicative linear functionals on a unital Banach algebra through the scalar identity . We develo…
Herglotz representation for operator-valued function on a set associated with test functions
Mainak Bhowmik, Poornendu Kumar
The Herglotz representation theorem for holomorphic functions with non-negative real part is a fundamental result in the theory of holomorphic functions. In this paper, we reinterp…
Operator Theory on the Pentablock
Abhay Jindal, Poornendu Kumar
The pentablock, denoted as $\cP,$ is defined as follows: $$\cP= \left\{ (a_{21}, {\rm tr}(A), {\rm det}(A)) : A = [a_{ij}]_{2 \times 2} \text{ with } \|A\|<1 \right\}.$$ It origina…