论文标题
正交$ \ ell_1 $ -set和von Neumann代数预期的极端非阿伦斯
Orthogonal $\ell_1$-sets and extreme non-Arens regularity of preduals of von Neumann algebras
论文作者
论文摘要
我们为Banach代数$ \ Mathfrak {a} $提出了一个新的定义，即常规，即商的$ \ Mathfrak {a}^\ ast/\ ast/\ ast/\ mathscr {wap} {wap}（\ mathfrak {a a}）$几乎是$ \ mathfrak的空间$ \ mathfrak {a}^\ ast。$的同构副本比Granirer在90年代引入的原始定义更简单，更正式。 然后，我们确定von Neumann代数$ \ Mathfrak {v} $的预先$ \ mathfrak {v} _ \ ast $的足够条件，从这种新意义上讲是非常非侵略的。这些条件是在$ \ mathfrak {v} _ \ ast的正交$ \ ell_1 $ -set的帮助下获得的。 我们表明，谐波分析中的一些主要代数满足了这些条件。其中有 $ {\ small \ bullet} $任何弱取消的离散的semigroup的加权半群代数，对于任何对角线的重量， $ {\ small \ bullet} $任何非污点的加权组代数， $ {\ small \ bullet} $任何本地紧凑的无限组的加权度量代数，对于任何对角线的重量， $ {\ small \ bullet} $，其本地紧凑型无限组的傅立叶代数大于或等于其紧凑的覆盖号码， $ {\ small \ bullet} $包含无限amenable子组的任何可数离散组的傅立叶代数。
We propose a new definition for a Banach algebra $\mathfrak{A}$ to be extremely non-Arens regular, namely that the quotient $\mathfrak{A}^\ast/\mathscr{WAP}(\mathfrak{A})$ of $\mathfrak{A}^\ast$ with the space of its weakly almost periodic elements contains an isomorphic copy of $\mathfrak{A}^\ast.$ This definition is simpler and formally stronger than the original one introduced by Granirer in the nineties. We then identify sufficient conditions for the predual $\mathfrak{V}_\ast$ of a von Neumann algebra $\mathfrak{V}$ to be extremely non-Arens regular in this new sense. These conditions are obtained with the help of orthogonal $\ell_1$-sets of $\mathfrak{V}_\ast.$ We show that some of the main algebras in Harmonic Analysis satisfy these conditions. Among them,there is ${\small \bullet}$ the weighted semigroup algebra of any weakly cancellative discrete semigroup, for any diagonally bounded weight, ${\small \bullet}$ the weighted group algebra of any non-discrete locally compact infinite group and for any weight, ${\small \bullet}$ the weighted measure algebra of any locally compact infinite group, for any diagonally bounded weight, ${\small \bullet}$ the Fourier algebra of any locally compact infinite group having its local weight greater or equal than its compact covering number, ${\small \bullet}$ the Fourier algebra of any countable discrete group containing an infinite amenable subgroup.
