Invariant subspaces of idempotents on Hilbert spaces

2022/04/26 by Neeru Bala, Bala, Neeru, Nirupam Ghosh +3 · 1 citation
Mathematics · #15A60 #46B50 #47A15 #47B10 #47B15 #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Operator Algebras (math.OA) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2204.12222

openalex publication_date 2022/04/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In the setting of operators on Hilbert spaces, we prove that every quasinilpotent operator has a non-trivial closed invariant subspace if and only if every pair of idempotents with a quasinilpotent commutator has a non-trivial common closed invariant subspace. We also present a geometric characterization of invariant subspaces of idempotents and classify operators that are essentially idempotent.

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