Vol. 37, No. 3, 1971

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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