Intertwining operators between different Hilbert spaces: connection with frames

TL;DR

This paper explores the use of intertwining operators to construct (almost) isospectral self-adjoint operators across different Hilbert spaces, with applications rooted in frame theory and g-frames.

Contribution

It extends previous methods to create isospectral operators in different Hilbert spaces, connecting intertwining operators with frame and g-frame theories.

Findings

Constructed (almost) isospectral operators in different Hilbert spaces.

Provided detailed examples from frame and g-frame theories.

Extended previous intertwining operator strategies.

Abstract

In this paper we generalize a strategy recently proposed by the author concerning intertwining operators. In particular we discuss the possibility of extending our previous results in such a way to construct (almost) isospectral self-adjoint operators living in different Hilbert spaces. Many examples are discussed in details. Many of them arise from the theory of frames in Hilbert spaces, others from the so-called g-frames.