|
|||||
|
|
|
|
|
|
|
|
|
On k-shrinking and k-boundedly complete basic sequences and
quasi-reflexive spaces
Leonard Paul Sternbach |
|
Vol. 37 (1971), No. 3, 817–823
|
Abstract |
|
A Banach space X is called quasi-reflexive (of order n) if codimX∗∗π(X) < +∞(codimX∗∗π(X) = n), where π denotes the canonical embedding of X into its second conjugate x∗∗. R. Herman and R. Whitley have shown that every quasireflexive space contains an infinite dimensional reflexive subspace. In this paper this result is extended by showing that if X is quasi-reflexive of order n and 0 ≦ k ≦ n then X contains a subspace which is quasi-reflexive of order k. |
Mathematical Subject Classification 2000
Primary: 46B15
|
Milestones
Received: 2 September 1969
Revised: 15 September 1970
Published: 1 June 1971
|
Authors |
| Leonard Paul Sternbach | |
|
