Arup Chattopadhyay

Trace Formulae in Operator Theory

In this article, we survey several kinds of trace formulas that one encounters in the theory of single and multi-variable operators. We give some sketches of the proofs, often based on the principle of finite-dimensional approximations to the objects at hand in the formulas.

A New Proof of the Helton–Howe–Carey–Pincus Trace Formula

In this article, we give an alternative proof of the Helton–Howe–Carey–Pincus trace formula using Krein’s trace formula.

On submajorization and eigenvalue inequalities

Let be the algebra of complex matrices and let be a completely positive map. Suppose is a self-adoint matrix. We prove a submajorization result concerning positive and negative parts of the spectrum of . As a consequence, we obtain inequalities concerning the smallest and the largest eigenvalues of the Schur product of and , where and are self-adjoint.