Complex symmetric operator acting between two different Hilbert spaces

TL;DR

This paper introduces the study of complex symmetric operators acting between two different Hilbert spaces and explores their properties, including the closure of this class under various topologies.

Contribution

It initiates the analysis of complex symmetric operators between distinct Hilbert spaces and characterizes their closure properties.

Findings

Computed the closure of CSO under various topologies.

Established foundational properties of these operators.

Laid groundwork for further research in this area.

Abstract

This paper will initiate a study on the class of complex symmetric operators acting between two different Hilbert space. Among other things, we compute the closure of CSO with respect to the several topologies.