On the Canonical Calkin Reduction Operator

This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Submitted: 2024-12-18; Published: 2024-12-18

This work is licensed under Creative Commons Attribution–NonCommercial International License (CC BY-NC 4.0).

Abstract

The topic of discussion here is the reduction operator of Calkin and his methodof extensions of a Hermitian operator, variant from the von Neumann theory. Anexistence of a partial isometric reduction operator is established, which providesa link between these theories, and referred to as the canonical reduction operator.Concrete realization of discussed is applied to a canonical differential operator.