A version of Lomonosov's theorem for collections of positive operators
| dc.creator | Popov, Alexey I. | |
| dc.creator | Troitsky, Vladimir G. | |
| dc.date | 2008-07-21 | |
| dc.date.accessioned | 2026-07-07T09:51:53Z | |
| dc.date.available | 2026-07-07T09:51:53Z | |
| dc.description | It is known that for every Banach space X and every proper WOT-closed subalgebra A of L(X), if A contains a compact operator then it is not transitive. That is, there exist non-zero x in X and f in X* such that f(Tx)=0 for all T in A. In the case of algebras of adjoint operators on a dual Banach space, V.Lomonosov extended this as follows: without having a compact operator in the algebra, |f(Tx)| is less than or equal to the essential norm of the pre-adjoint operator T_* for all T in A. In this paper, we prove a similar extension (in case of adjoint operators) of a result of R.Drnovsek. Namely, we prove that if C is a collection of positive adjoint operators on a Banach lattice X satisfying certain conditions, then there exist non-zero positive x in X and f in X* such that f(Tx) is less than or equal to the essential norm of T_* for all T in C. | |
| dc.identifier | https://arxiv.org/abs/0807.3327 | |
| dc.identifier | http://arxiv.org/abs/0807.3327 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/165402 | |
| dc.subject | Functional Analysis | |
| dc.subject | Operator Algebras | |
| dc.subject | 47B65; 47A15 | |
| dc.title | A version of Lomonosov's theorem for collections of positive operators | |
| dc.type | text |