Some Open Problems and Conjectures Associated with the Invariant Subspace Problem View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2005-09

AUTHORS

Y. A. Abramovich, C. D. Aliprantis, G. Sirotkin, V. G. Troitsky

ABSTRACT

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 Prilozhen7(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 More... »

PAGES

273-286

References to SciGraph publications

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s11117-004-3786-9

DOI

http://dx.doi.org/10.1007/s11117-004-3786-9

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1037840348


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147 rdf:type schema:Organization
148 https://www.grid.ac/institutes/grid.261128.e schema:alternateName Northern Illinois University
149 schema:name Department of Mathematics, Northern Illinois University, 60115, DeKalb, IL, USA
150 rdf:type schema:Organization
 




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