Bala, Neeru ; Ghosh, Nirupam ; Sarkar, Jaydeb (2022) Invariant Subspaces of Idempotents on Hilbert Spaces Integral Equations and Operator Theory, 95 (1). ISSN 0378-620X
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Official URL: https://doi.org/10.1007/s00020-022-02723-2
Related URL: http://dx.doi.org/10.1007/s00020-022-02723-2
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.
| Item Type: | Article |
|---|---|
| Source: | Copyright of this article belongs to Springer. |
| Keywords: | Idempotents; Orthogonal projections; Invariant subspaces; Quasinilpotent operators; Essentially idempotent operators; Commutators. |
| ID Code: | 140592 |
| Deposited On: | 29 Dec 2025 11:16 |
| Last Modified: | 29 Dec 2025 11:16 |
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