The unbounded commutant of an operator of class C_0

TL;DR

This paper characterizes the unbounded commutant of a class C_0 operator using bounded operators, extending previous results for specific defect indices.

Contribution

It generalizes the description of the unbounded commutant for class C_0 operators beyond known cases with defect index 1 or finite index.

Findings

Extended Sarason's results to arbitrary finite defect indices.

Provided a description of unbounded commutants in terms of bounded operators.

Generalized previous theorems for class C_0 operators.

Abstract

We describe the closed, densely defined linear transformations commuting with a given operator T of class C_0 in terms of bounded operators in {T}'. Our results extend those of Sarason for operators with defect index 1, and Martin in the case of arbitrary finite index.