论文标题
八面体规范
Octahedral norms in free Banach lattices
论文作者
论文摘要
在本文中，我们在免费的Banach Lattices $ fbl [e] $中研究了由Banach Space $ E $生成的八面体规范。我们证明，如果$ e $是$ l_1（μ）$ - 空间，则是von Neumann代数的前提，这是JBW $^*$ - 三重，$ m $ m $ bashach space的双重，碟片代数，或者是投影量的张力产品，或者在某些假设下，然后是$ fbl [e] $ fbl [e]。当$ e $的拓扑双$ e^*$几乎是正方形时，我们会得到类似的结果。我们通过证明由尺寸$ \ geq 2 $产生的免费Banach晶格的规范完成了纸张，这是无处可区分的。此外，我们讨论了有关此主题的一些开放问题。
In this paper, we study octahedral norms in free Banach lattices $FBL[E]$ generated by a Banach space $E$. We prove that if $E$ is an $L_1(μ)$-space, a predual of von Neumann algebra, a predual of a JBW$^*$-triple, the dual of an $M$-embedded Banach space, the disc algebra or the projective tensor product under some hypothesis, then the norm of $FBL[E]$ is octahedral. We get the analogous result when the topological dual $E^*$ of $E$ is almost square. We finish the paper by proving that the norm of the free Banach lattice generated by a Banach space of dimension $ \geq 2$ is nowhere Fréchet differentiable. Moreover, we discuss some open problems on this topic.
