Invariant subspaces of idempotents on Hilbert spaces
Functional Analysis
2022-04-27 v1 Operator Algebras
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.
Keywords
Cite
@article{arxiv.2204.12222,
title = {Invariant subspaces of idempotents on Hilbert spaces},
author = {Neeru Bala and Nirupam Ghosh and Jaydeb Sarkar},
journal= {arXiv preprint arXiv:2204.12222},
year = {2022}
}
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15 pages