论文标题
Banach太空巢代数的双模型
Bimodules of Banach space nest algebras
论文作者
论文摘要
我们扩展到Banach Space Nest代数，其双模型的基本支撑和支撑功能对的理论，从而获得了Hilbert Space Nest代数的长期确定结果的Banach空间对应物。也就是说，给定一个Banach Space Nest代数$ \ Mathcal a $，我们为具有给定的基本支持功能或支持功能对的最大和最小$ \ Mathcal赋予了最小$ \ Mathcal。这些特征是完整的，除了最小$ \ Mathcal A $ bimodule与支持功能对相对应，在这种情况下，我们取得了一些进展。 我们还表明，Banach太空巢代数的弱闭合的双模模恰好是反身操作员空间的双模模。为此，我们至关重要的是，反身双模型决定了一定类别的一类可接受的支持函数。
We extend to Banach space nest algebras the theory of essential supports and support function pairs of their bimodules, thereby obtaining Banach space counterparts of long established results for Hilbert space nest algebras. Namely, given a Banach space nest algebra $\mathcal A$, we charaterise the maximal and the minimal $\mathcal A$-bimodules having a given essential support function or support function pair. These characterisations are complete except for the minimal $\mathcal A$-bimodule corresponding to a support function pair, in which case we make some headway. We also show that the weakly closed bimodules of a Banach space nest algebra are exactly those that are reflexive operator spaces. To this end, we crucially prove that reflexive bimodules determine uniquely a certain class of admissible support functions.
