Multiplication operators on L(L_p) and $\ell_p$-strictly singular operators
| dc.creator | Johnson, William B. | |
| dc.creator | Schechtman, Gideon | |
| dc.date | 2007-08-03 | |
| dc.date.accessioned | 2026-07-07T08:22:06Z | |
| dc.date.available | 2026-07-07T08:22:06Z | |
| dc.description | A classification of weakly compact multiplication operators on L(L_p), $1<p<\infty$, is given. This answers a question raised by Saksman and Tylli in 1992. The classification involves the concept of $\ell_p$-strictly singular operators, and we also investigate the structure of general $\ell_p$-strictly singular operators on L_p. The main result is that if an operator T on L_p, 1<p<2, is $\ell_p$-strictly singular and T_{|X} is an isomorphism for some subspace X of L_p, then X embeds into L_r for all r<2, but X need not be isomorphic to a Hilbert space. It is also shown that if T is convolution by a biased coin on L_p of the Cantor group, $1\le p <2$, and $T_{|X}$ is an isomorphism for some reflexive subspace X of L_p, then X is isomorphic to a Hilbert space. The case p=1 answers a question asked by Rosenthal in 1976. | |
| dc.identifier | https://arxiv.org/abs/0708.0560 | |
| dc.identifier | http://arxiv.org/abs/0708.0560 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/135540 | |
| dc.subject | Functional Analysis | |
| dc.subject | 46B20, 46E30 | |
| dc.title | Multiplication operators on L(L_p) and $\ell_p$-strictly singular operators | |
| dc.type | text |