A Short Proof of Von Neumann’s Conjecture

Bahman Mashood^1,

¹66 Shipely Avenue, Daly City, CA 94015, US

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

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:
Hilbert space bounded operator invariant subspace polynomial orthogonal basis

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References:

[1]	R. Abraham, J.E. Mardsen, T.Ratiu. “Manifolds, Tensor Analysis and applications”.
[2]	Jonathan Noel, “The invariant subspace problem”, Thesis, Department of Mathematics and Statistic, Thompson River University, 2011.