TOPOLOGIES ON THE SET OF ALL SUBSPACES OF A BANACH SPACE AND RELATED QUESTIONS OF BANACH SPACE GEOMETRY

Abstract

The survey is devoted to two of the most common topologies on the set of all subspaces of a Banach space. The first part contains definitions of the topologies and a description of their properties. The main topics of the rest of the paper are: (1) Comparison of the introduced topologies; (2) Stability of properties of subspaces with respect to the topologies. The last section contains a list of open problems