We show that a Banach space X has a basis provided there are bounded linear finite rank operators R n : X Ä X such that lim n R n x=x for all x # X, R m R n =R min(m, n) if m{n, and R n &R n&1 factors uniformly through l mn p 's for some p. As an application we obtain conditions on a subset 4/Z such
Spaces with σ-point finite bases
✍ Scribed by W.N. Hunsaker; W.F. Lindgren
- Publisher
- Elsevier Science
- Year
- 1978
- Weight
- 471 KB
- Volume
- 8
- Category
- Article
- ISSN
- 0016-660X
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