From the introduction (translated from the Chinese): ``So far, very little is known about the structure of rings of continuous linear transformations. In this paper we use our orthogonalization theorem [the author, Sci. Sinica Ser. A {\bf 27} (1984), no. 10, 1009--1017; MR0795921 (87c:16010a)] to determine the structure of the complete ring of continuous linear transformations of a countably infinite-dimen-\break sional vector space. The case of an arbitrary infinite-dimensional vector space appears to be extremely difficult.''