Some Open Problems and Conjectures Associated with the Invariant Subspace Problem

Autor:	Y.A. Abramovich, Vladimir G. Troitsky, Charalambos D. Aliprantis, Gleb Sirotkin
Rok vydání:	2005
Předmět:	Mathematics::Functional Analysis Approximation property General Mathematics Spectrum (functional analysis) Invariant subspace Banach manifold Finite-rank operator Compact operator Theoretical Computer Science Algebra C0-semigroup Invariant subspace problem Analysis Mathematics
Zdroj:	Positivity. 9:273-286
ISSN:	1572-9281 1385-1292
DOI:	10.1007/s11117-004-3786-9
Popis:	There is a subtle difference as far as the invariant subspace problem is concerned for operators acting on real Banach spaces and operators acting on complex Banach spaces. For instance, the classical hyperinvariant subspace theorem of Lomonosov [Funktsional. Anal. nal. i Prilozhen 7(3)(1973), 55–56. (Russian)], while true for complex Banach spaces is false for real Banach spaces. When one starts with a bounded operator on a real Banach space and then considers some “complexification technique” to extend the operator to a complex Banach space, there seems to be no pattern that indicates any connection between the invariant subspaces of the “real” operator and those of its “complexifications.” The purpose of this note is to examine two complexification methods of an operator T acting on a real Banach space and present some questions regarding the invariant subspaces of T and those of its complexifications
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::3124ea458a0c8fdd7a29eee0e9629c8d https://doi.org/10.1007/s11117-004-3786-9 Zobrazit plný text záznamu Full text from SpringerLink