Let X be a Banach space. Then there is a locally convex topology for X, the "Right topology," such that a linear map T, from X into a Banach space Y, is weakly compact, precisely when T is a continuous map from X, equipped with the "Right" topology, into Y equipped with the norm topology. When T is only sequentially continuous with respect to the Right topology, it is said to be pseudo weakly compact. This notion is related to Pelczynski's Property (V). (c) 2006 Elsevier Inc. All rights reserved.
|Number of pages||7|
|Journal||Journal of Mathematical Analysis and Applications|
|Early online date||23 Mar 2006|
|Publication status||Published - 15 Jan 2007|
- weakly compact operators
- right topology
- Mackey topology