Next Article in Journal
Unit-Power Half-Normal Distribution Including Quantile Regression with Applications to Medical Data
Next Article in Special Issue
Approximation and the Multidimensional Moment Problem
Previous Article in Journal
Probabilistic Perturbation Bounds for Invariant, Deflating and Singular Subspaces
Previous Article in Special Issue
On the Approximation of the Hardy Z-Function via High-Order Sections
 
 
Journal Notice: The Editorial Office is aware of the concerns raised regarding the paper and are currently investigating this matter in collaboration with members of the Editorial Board.
Font Type:
Arial Georgia Verdana
Font Size:
Aa Aa Aa
Line Spacing:
Column Width:
Background:
Article

The Invariant Subspace Problem for Separable Hilbert Spaces

by
Roshdi Khalil
1,*,
Abdelrahman Yousef
2,
Waseem Ghazi Alshanti
3 and
Ma’mon Abu Hammad
3
1
Department of Mathematics, The University of Jordan, Amman 11942, Jordan
2
Department of Mathematics & Statistics, American University of Sharjah, Sharjah P.O. Box 26666, United Arab Emirates
3
Department of Mathematics, Al Zaytoonah University of Jordan, Amman 11733, Jordan
*
Author to whom correspondence should be addressed.
Axioms 2024, 13(9), 598; https://doi.org/10.3390/axioms13090598
Submission received: 31 July 2024 / Revised: 27 August 2024 / Accepted: 28 August 2024 / Published: 2 September 2024
(This article belongs to the Special Issue Numerical Methods and Approximation Theory)

Abstract

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.
Keywords: invariant subspace problem; separable Hilbert space; orbits of operators; orthogonal complement invariant subspace problem; separable Hilbert space; orbits of operators; orthogonal complement

Share and Cite

MDPI and ACS Style

Khalil, R.; Yousef, A.; Alshanti, W.G.; Hammad, M.A. The Invariant Subspace Problem for Separable Hilbert Spaces. Axioms 2024, 13, 598. https://doi.org/10.3390/axioms13090598

AMA Style

Khalil R, Yousef A, Alshanti WG, Hammad MA. The Invariant Subspace Problem for Separable Hilbert Spaces. Axioms. 2024; 13(9):598. https://doi.org/10.3390/axioms13090598

Chicago/Turabian Style

Khalil, Roshdi, Abdelrahman Yousef, Waseem Ghazi Alshanti, and Ma’mon Abu Hammad. 2024. "The Invariant Subspace Problem for Separable Hilbert Spaces" Axioms 13, no. 9: 598. https://doi.org/10.3390/axioms13090598

APA Style

Khalil, R., Yousef, A., Alshanti, W. G., & Hammad, M. A. (2024). The Invariant Subspace Problem for Separable Hilbert Spaces. Axioms, 13(9), 598. https://doi.org/10.3390/axioms13090598

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

Article Metrics

Back to TopTop