Urysohn's operators are a very important kind of nonlinear operators. Many scholars investigated their properties in various spaces. Similar to Urysohn's operators, a kind of nonlinear operators is introduced,...Urysohn's operators are a very important kind of nonlinear operators. Many scholars investigated their properties in various spaces. Similar to Urysohn's operators, a kind of nonlinear operators is introduced, and their continuity and complete continuity in a kind of Fenchel-Orlicz spaces are discussed in this paper. The results obtained are a generalization of the corresponding results in [1-4].展开更多
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
文摘Urysohn's operators are a very important kind of nonlinear operators. Many scholars investigated their properties in various spaces. Similar to Urysohn's operators, a kind of nonlinear operators is introduced, and their continuity and complete continuity in a kind of Fenchel-Orlicz spaces are discussed in this paper. The results obtained are a generalization of the corresponding results in [1-4].
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^∞.
