| Abstract: | In this paper we present four methods to generate three-space BANACH space ideals. They are based on the concept of total incomparability of H. P. ROSENTHAL and on a dual concept, total coincomparability, which is here introduced. We use the assertion that the sum of two totally incomparable closed subspaces of a BANACH space is norm-closed, which is shown by means of an easier and more natural proof than that of ROSENTHAL [10], and an analogous property about the total coincomparability. Several well-known ideals are obtained with the above methods, and so they are three-space ideals. |
