In this paper, we show that any a-complete Banach lattice, with a σ-order semicontinuous but not σ-order continuous norm, contains an asymptotically isometric copy of l^∞. We also get that the Fenchel-Orlicz space ...In this paper, we show that any a-complete Banach lattice, with a σ-order semicontinuous but not σ-order continuous norm, contains an asymptotically isometric copy of l^∞. We also get that the Fenchel-Orlicz space with the Orlicz norm may not contain an asymptotically isometric copy of l^∞.展开更多
基金the National Natural Science Foundation of China （Nos. 10571090 Foundation of Nankai University.
文摘In this paper, we show that any a-complete Banach lattice, with a σ-order semicontinuous but not σ-order continuous norm, contains an asymptotically isometric copy of l^∞. We also get that the Fenchel-Orlicz space with the Orlicz norm may not contain an asymptotically isometric copy of l^∞.
