An invariant subspace problem for multilinear operators on Banach spaces and algebras

Journal of inequalities and applications

John Emenyu¹ 

关键词: Banach spaces;    invariant subspaces;    strongly invariant subspaces;    multilinear and polynomial operators;   

DOI  :  10.1186/s13660-016-1120-2

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

This paper is concerned with the study of invariant subspace problems for nonlinear operators on Banach spaces/algebras. Our study reveals that one faces unprecedented challenges such as lack of vector space structure and unbounded spectral sets when tackling invariant subspace problems for nonlinear operators via spectral information. To bypass some of these challenges, we modified an eigenvalue problem for nonlinear operators to cater for the structural properties of nonlinear operators and then established that nonlinear operators of finite type on a complex Banach algebra have nontrivial invariant subspaces.

【 授权许可】

CC BY