On bases, finite dimensional decompositions and weaker structures in Banach spaces Academic Article uri icon

abstract

  • This is an investigation of the connections between bases and weaker structures in Banach spaces and their duals. It is proved, e.g., that X has a basis if X* does, and that if X has a basis, then X* has a basis provided that X* 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 separable ℒ p space has a basis. © 1971 The Weizmann Science Press of Israel.

author list (cited authors)

  • Johnson, W. B., Rosenthal, H. P., & Zippin, M.

citation count

  • 128

complete list of authors

  • Johnson, WB||Rosenthal, HP||Zippin, M

publication date

  • February 1971