Boundary functions form a useful tool in the study of ideals in various classes of nest algebras. In the simplest case, where the nest algebra is T_n, the algebra of n x n upper triangular matrices, it is a simple matter to associate to each ideal in T_n an appropriate boundary function. This was generalized to weakly closed ideals in general nest subalgebras of B(H) by Erdos and Power in [EP] and to Volterra nest subalgebras of C~*-algebras by Power in [PI]. Larson and Solel extended the Erdos-Power theory to the context of nest subalgebras of factor von Neumann algebras [LS]. Both theories apply to modules over the nest algebra, not just to ideals in the nest algebra. Davidson, Donsig and Hudson in [DDH] study support functions for norm closed bimodules of nest algebras; their support functions come in pairs which allow the determination of a maximal and sometimes a minimal bimodule for a given pair.
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机译：边界函数是研究各种嵌套代数中的理想情况的有用工具。在最简单的情况下，嵌套代数为T_n，即n x n个上三角矩阵的代数，将一个适当的边界函数与T_n中的每个理想关联起来是一件简单的事情。在[EP]中，这由Erdos和Power推广到B（H）的一般嵌套子代数中的弱封闭理想，在[PI]中由Power将其推广到C〜*代数的Volterra嵌套子代数。 Larson和Solel将Erdos-Power理论扩展到因子von Neumann代数[LS]的嵌套子代数的上下文中。两种理论都适用于嵌套代数上的模块，而不仅适用于嵌套代数中的理想。 [DDH]中的Davidson，Donsig和Hudson研究了巢代数的范数封闭双模的支持函数。它们的支持功能成对出现，从而可以确定给定对的最大双模数，有时甚至是最小双模数。
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