Notes on the Chernoff Product Formula

TL;DR

This paper revises and extends the Chernoff product formula in a Hilbert space, achieving convergence in the operator-norm topology, with focus on self-adjoint and quasi-sectorial contractions.

Contribution

It provides a strengthened version of the Chernoff product formula with operator-norm convergence, expanding its applicability to self-adjoint and nonself-adjoint cases.

Findings

Achieved operator-norm convergence for the Chernoff product formula.

Extended the formula to quasi-sectorial contractions.

Provided new insights into the convergence behavior in Hilbert spaces.

Abstract

We revise the strong convergent Chernoff product formula and extend it, in a Hilbert space, to convergence in the operator-norm topology. Main results deal with the self-adjoint Chernoff product formula. The nonself-adjoint case concerns the quasi-sectorial contractions.