A pseudo-Daugavet property for narrow projections in Lorentz spaces
| dc.creator | Popov, Mikhail M. | |
| dc.creator | Randrianantoanina, Beata | |
| dc.date | 2001-10-16 | |
| dc.date.accessioned | 2026-07-07T04:43:52Z | |
| dc.date.available | 2026-07-07T04:43:52Z | |
| dc.description | Let $X$ be a rearrangement-invariant space. An operator $T: X\to X$ is called narrow if for each measurable set $A$ and each $ε> 0$ there exists $x \in X$ with $x^2= χ_A, \int x d μ= 0$ and $\| Tx \| < ε$. In particular all compact operators are narrow. We prove that if $X$ is a Lorentz function space $L_{w,p}$ on [0,1] with $p>2$, then there exists a constant $k_X>1$ so that for every narrow projection $P$ on $L_{w,p}$ $\| Id - P \| \geq k_X. $ This generalizes earlier results on $L_p$ and partially answers a question of E. M. Semenov. Moreover we prove that every rearrangement-invariant function space $X$ with an absolutely continuous norm contains a complemented subspace isomorphic to $X$ which is the range of a narrow projection and a non-narrow projection, which gives a negative answer to a question of A.Plichko and M.Popov. | |
| dc.description | 24 pages | |
| dc.identifier | https://arxiv.org/abs/math/0110168 | |
| dc.identifier | http://arxiv.org/abs/math/0110168 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/62406 | |
| dc.subject | Functional Analysis | |
| dc.subject | 46B20, 46E30, 46C15 | |
| dc.title | A pseudo-Daugavet property for narrow projections in Lorentz spaces | |
| dc.type | text |