Invariant Subspaces of Idempotents on Hilbert Spaces

Authors

Neeru Bala, Indian Statistical Institute Bangalore
Nirupam Ghosh, Indian Statistical Institute Bangalore
Jaydeb Sarkar, Indian Statistical Institute Bangalore

Article Type

Research Article

Publication Title

Integral Equations and Operator Theory

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.

DOI

https://10.1007/s00020-022-02723-2

Publication Date

3-1-2023

Comments

Open Access, Green

Recommended Citation

Bala, Neeru; Ghosh, Nirupam; and Sarkar, Jaydeb, "Invariant Subspaces of Idempotents on Hilbert Spaces" (2023). Journal Articles. 3833.
https://digitalcommons.isical.ac.in/journal-articles/3833