On the norm closure problem for complex symmetric operators

TL;DR

This paper demonstrates that the collection of all complex symmetric operators on an infinite-dimensional Hilbert space is not closed under the operator norm topology, highlighting a fundamental topological property of these operators.

Contribution

It establishes that the set of complex symmetric operators is not norm closed, providing new insights into their topological structure.

Findings

The set of complex symmetric operators is not norm closed.

This result impacts the understanding of operator topologies.

It advances the theory of complex symmetric operators.

Abstract

We prove that the set of all complex symmetric operators on a separable, infinite-dimensional Hilbert space is not norm closed.