On bases, finite dimensional decompositions and weaker structures in Banach spaces
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This is an investigation of the connections between bases and weaker structures in Banach spaces and their duals. It is proved, e.g., thatX has a basis ifX* does, and that ifX has a basis, thenX* has a basis provided thatX* is separable and satisfies Grothendieck’s approximation property; analogous results are obtained concerning π-structures and finite dimensional Schauder decompositions. The basic results are then applied to show that every separableℒ p space has a basis.
KeywordsBanach Space Approximation Property Natural Projection Separable Banach Space Invertible Operator
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- 1.M. M. Day,Normed Linear Spaces, Springer, 1958.Google Scholar
- 2.N. Dunford and J. T. Schwartz,Linear operators, Part I, New York, 1958.Google Scholar
- 3.A. Grothendieck,Produits tensoriels topologiques et espaces nucléaires, Mem. Amer. Math. Soc.16 (1955).Google Scholar
- 4.W. B. Johnson,Finite dimensional Schauder decompositions in θλ and dual θλ spaces, Illinois J. Math. (to appear).Google Scholar
- 5.W. B. Johnson,On the existence of strongly series summable Markuschevich bases in Banach spaces (to appear).Google Scholar
- 7.J. Lindenstrauss,Extension of compact operators, Mem. Amer. Math. Soc.48 (1964).Google Scholar
- 8.J. Lindenstrauss,On James’ paper “Separable conjugate spaces” (to appear).Google Scholar
- 13.A. Pełczyński and P. Wojtaszczyk,Banach spaces with finite dimensional expansions of identity and universal bases of finite dimensional subspaces, Studia Math. (to appear).Google Scholar