Invariant subspace problem in Hilbert space: Correlation with the Kadison-Singer problem and the Borel conjecture

2023/08/31 by Mostafa Behtouei, Behtouei, Mostafa · 1 citation
Computer Science · Mathematics · #Advanced Algebra and Logic #Advanced Operator Algebra Research #FOS: Physical sciences #Functional Equations Stability Results #Mathematical Physics (math-ph)

paper · pdf · doi:10.48550/arxiv.2309.00171

openalex publication_date 2023/08/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper explores the intriguing connections between the invariant subspace problem, the Kadison-Singer problem, and the Borel conjecture. The Kadison-Singer problem, originally formulated in terms of pure states on C*-algebras, was later reformulated using projections, establishing a link with the invariant subspace problem. The Borel conjecture, a question in descriptive set theory, connects to the invariant subspace problem through Borel equivalence relations. This paper elucidates these connections, underscoring the interplay of unsolved mathematical problems and the collaborative nature of mathematical research.

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