On Equivalence and Linearization of Operator Matrix Functions with Unbounded Entries

TL;DR

This paper develops new theoretical results on the equivalence and linearization of unbounded operator matrix functions, introducing generalized concepts and methods for simplifying complex operator functions.

Contribution

It introduces a generalized notion of equivalence after extension and provides methods to find equivalences and linearizations for unbounded operator matrix functions.

Findings

Established equivalence results for unbounded operator functions

Developed methods to linearize operator matrix functions

Provided techniques to relate operator matrix functions to their entries

Abstract

In this paper we present equivalence results for several types of unbounded operator functions. A generalization of the concept equivalence after extension is introduced and used to prove equivalence and linearization for classes of unbounded operator functions. Further, we deduce methods of finding equivalences to operator matrix functions that utilizes equivalences of the entries. Finally, a method of finding equivalences and linearizations to a general case of operator matrix polynomials is presented.