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
Relative bases in Banach spaces
✍ Scribed by Yılmaz Yılmaz
- Publisher
- Elsevier Science
- Year
- 2009
- Tongue
- English
- Weight
- 522 KB
- Volume
- 71
- Category
- Article
- ISSN
- 0362-546X
No coin nor oath required. For personal study only.
📜 SIMILAR VOLUMES
We begin by giving, in Section 1, a number of conditions including compactness and weak sequential continuity, which are equivalent to the existence of monomial bases. We apply these equivalences and the Gon-zalo᎐Jaramillo indexes to the problem of existence of monomial bases in spaces of multilinea
## Abstract In the present paper we give conditions for Banach spaces of absolutely __p__‐summing operators to have unconditional bases. In this case we obtain methods to estimate the π~__p__~‐norm. Also we consider spaces of absolutely __p__‐summing operators with “bad” structure, i.e., without lo
## Abstract We develop some parts of the theory of compact operators from the point of view of computable analysis. While computable compact operators on Hilbert spaces are easy to understand, it turns out that these operators on Banach spaces are harder to handle. Classically, the theory of compac