On unbounded complementable operators

TL;DR

This paper extends the concept of complementability from bounded to unbounded densely defined operators on Hilbert spaces, offering new structural insights and analytical techniques in operator theory.

Contribution

It introduces a framework for analyzing complementability of unbounded operators, expanding the theoretical understanding beyond bounded cases.

Findings

Developed a projection-based framework for unbounded operators

Provided new structural insights into unbounded operator complementability

Enhanced the theoretical tools for operator analysis

Abstract

The concept of complementability is extended from bounded operators to densely defined operators on Hilbert spaces. By introducing appropriate projections and decomposition techniques, a framework is developed for analyzing complementability in this broader context. The results provide new insights into the structure of unbounded operators, contributing to the ongoing development of operator theory.