巴拿赫空间中的等距逼近与延拓理论及其应用

This program of Fundation is to study the problems of isometric approximation and isometric extension. Since the nice specialities of isometric(equidistant).mapping, they are very useful subjects to research that whether a isometric mapping defined a local region can be extended to whole Banach space, under what conditions is a “DOPP”(i.e. distance one preserving property) mapping can be a isometric mapping, and the approximation problem of the “almost isometric” operator by isometric operator, etc. In the past three years, we obtained some isometric extension theorems about some concrete Banach spaces, some relations between DOPP and isometric mapping in Hilbert space, and some results concerning the isometric approximation.

等距算子是理论与应用中最重要的一类算子。由于现实中不存在精确的等距算子，故研究其扰动理论（几乎等距算子）就十分必要；又因常常接触到的是局部区域上的等距算子，因而研究其（仿射）延拓问题就极有意义；此外。各种空间上的等距算子的表现理论、等距同构与嵌入理论及等距算子在数学各专题上的应用均是我们研究的内容。