[SunkenCiv]

Thanks GOPJ. No one is crankier than a vexed theorist.

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[AdmSmith]

Cool, it indicates that it is never too late for us to study complicated problems.

In case there are updates they will be published here:
On the invariant subspace problem in Hilbert spaces by Per H. Enflo https://arxiv.org/abs/2305.15442

with a discussion of the paper https://mathoverflow.net/questions/447664/understanding-a-simplifying-assumption-in-invariant-subspace-problem-proof

and a non-technical paper by Mostafa Behtouei:
Invariant Subspace Problem in Hilbert Spaces: Exploring Applications in Quantum Mechanics, Control Theory, Operator Algebras, Functional Analysis and Accelerator Physics

In conclusion, the invariant subspace problem is a fundamental question in operator theory with applications in various branches of mathematics and physics. Its
study provides insights into the behavior of linear operators, quantum systems, and
operator algebras. While the problem remains unsolved in many cases, it continues to stimulate research and uncover new connections between different areas of
mathematics.

https://arxiv.org/pdf/2306.17023.pdf