Email this article Invariant Subspaces for Commuting Operators on a Real Banach Space
- Authors: Lomonosov V.I.1, Shul’man V.S.2
-
Affiliations:
- Department of Mathematics, Kent State University
- Department of Higher Mathematics, Vologda State University
- Issue: Vol 52, No 1 (2018)
- Pages: 53-56
- Section: Brief Communications
- URL: https://journals.rcsi.science/0016-2663/article/view/234402
- DOI: https://doi.org/10.1007/s10688-018-0207-6
- ID: 234402
Cite item
Open Access
Access granted
Subscription Access
Abstract
It is proved that the commutative algebra A of operators on a reflexive real Banach space has an invariant subspace if each operator T ∈ A satisfies the condition
\({\left\| {1 - \varepsilon {T^2}} \right\|_e} \leqslant 1 + o\left( \varepsilon \right)as\varepsilon \searrow 0,\)![]()
where ║ · ║e denotes the essential norm. This implies the existence of an invariant subspace for any commutative family of essentially self-adjoint operators on a real Hilbert space.About the authors
V. I. Lomonosov
Department of Mathematics, Kent State University
Author for correspondence.
Email: lomonoso@mcs.kent.edu
United States, Kent
V. S. Shul’man
Department of Higher Mathematics, Vologda State University
Email: lomonoso@mcs.kent.edu
Russian Federation, Vologda
Supplementary files
