| Full text | |
| Author(s): |
Koszmider, P.
Total Authors: 1
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| Document type: | Journal article |
| Source: | JOURNAL OF APPLIED ANALYSIS; v. 11, n. 2, p. 19-pg., 2005-12-01. |
| Abstract | |
Classical results on weakly compactly generated (WCG) Banach spaces imply the existence of projectional resolutions of identity (PRI) and the existence of many projections on separable subspaces (SCP). We address the questions if these can be the only projections in a nonseparable WCG space, in the sense that there is a PRI (P-alpha: omega <= alpha <= lambda) such that any projection is the sum of an operator in the closure of the linear span of countably many P-alpha's (in the strong operator topology) and a separable range operator. Wark's modification of Shelah's and Steprans' construction provides an unconditional example for lambda = omega(1). We note that it is impossible for lambda > omega(2). (AU) | |