论文标题
Bishop的一些稳定性 - Phelps--Bollobáslipschitz地图的特性
Some stability properties for the Bishop--Phelps--Bollobás property for Lipschitz maps
论文作者
论文摘要
我们研究Lipschitz地图（LIP-BPB特性）的Bishop-Phelps-Bollobás属性的稳定性行为。该属性是Lipschitz版本的古典Bishop-Phelps-Bollobás属性，并处理了近似Lipschitz地图的可能性，该地图几乎通过Lipschitz地图在一对不同的点上达到了它的（Lipschitz）标准，这是通过Lipschitz地图在与以前的一对（相对）中的一对（相对）中非常近的。我们首先研究了该特性在域空间（度量）总和下的稳定性。接下来，我们研究何时可以将LIP-BPB属性从标量函数传递到一些矢量值图，从而获得与$γ$ -Flat Operators和$ ack $结构有关的一些积极结果。 对于Lipschitz紧凑地图，我们获得了更清晰的结果。还研究了针对目标空间的绝对总和的行为。我们还获得了与上述结果相似的结果，该结果涉及到了强烈的Quorm Chitchitz Maps和Lipschitz紧凑型地图的密度。
We study the stability behavior of the Bishop-Phelps-Bollobás property for Lipschitz maps (Lip-BPB property). This property is a Lipschitz version of the classical Bishop-Phelps-Bollobás property and deals with the possibility of approximating a Lipschitz map that almost attains its (Lipschitz) norm at a pair of distinct points by a Lipschitz map attaining its norm at a pair of distinct points (relatively) very closed to the previous one. We first study the stability of this property under the (metric) sum of the domain spaces. Next, we study when it is possible to pass the Lip-BPB property from scalar functions to some vector-valued maps, getting some positive results related to the notions of $Γ$-flat operators and $ACK$ structure. We get sharper results for the case of Lipschitz compact maps. The behaviour of the property with respect to absolute sums of the target space is also studied. We also get results similar to the above ones about the density of strongly norm attaining Lipschitz maps and of Lipschitz compact maps.
