The Invariant Subspace Problem for Separable Hilbert Spaces

Roshdi Khalil; Abdelrahman Yousef; Waseem Ghazi Alshanti; Ma’mon Abu Hammad

doi:10.3390/axioms13090598

Axioms (Sep 2024)

The Invariant Subspace Problem for Separable Hilbert Spaces

Roshdi Khalil,
Abdelrahman Yousef,
Waseem Ghazi Alshanti,
Ma’mon Abu Hammad

Affiliations

Roshdi Khalil: Department of Mathematics, The University of Jordan, Amman 11942, Jordan
Abdelrahman Yousef: Department of Mathematics & Statistics, American University of Sharjah, Sharjah P.O. Box 26666, United Arab Emirates
Waseem Ghazi Alshanti: Department of Mathematics, Al Zaytoonah University of Jordan, Amman 11733, Jordan
Ma’mon Abu Hammad: Department of Mathematics, Al Zaytoonah University of Jordan, Amman 11733, Jordan

DOI: https://doi.org/10.3390/axioms13090598
Journal volume & issue: Vol. 13, no. 9
p. 598

Abstract

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In this paper, we prove that every bounded linear operator on a separable Hilbert space has a non-trivial invariant subspace. This answers the well-known invariant subspace problem.

Published in Axioms

ISSN: 2075-1680 (Online)
Publisher: MDPI AG
Country of publisher: Switzerland
LCC subjects: Science: Mathematics
Website: http://www.mdpi.com/journal/axioms

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