Article citationsMore >>

R. Abraham, J.E. Mardsen, T.Ratiu. “Manifolds, Tensor Analysis and applications”.

has been cited by the following article:

Article

A Short Proof of Von Neumann’s Conjecture

166 Shipely Avenue, Daly City, CA 94015, US


American Journal of Mathematical Analysis. 2022, Vol. 10 No. 1, 1-2
DOI: 10.12691/ajma-10-1-1
Copyright © 2022 Science and Education Publishing

Cite this paper:
Bahman Mashood. A Short Proof of Von Neumann’s Conjecture. American Journal of Mathematical Analysis. 2022; 10(1):1-2. doi: 10.12691/ajma-10-1-1.

Correspondence to: Bahman  Mashood, 66 Shipely Avenue, Daly City, CA 94015, US. Email: b_mashood@hotmail.com

Abstract

Let H be a separable Hilbert space and let B(H) be the set of all bounded operators acting on H. Given T∈ B(H), we show that T has a proper invariant subspace, i.e., there exists a proper Hilbert subspace L⊂H such that T(L)⊆L. This problem has only been solved for special cases so far and in this article we try to offer a solution that can take care of the most general cases.

Keywords