Examples of hereditarily l¹ Banach spaces failing the Schur property

Parviz Azimi and James Neil Hagler

Vol. 122 (1986), No. 2, 287–297

DOI: 10.2140/pjm.1986.122.287

Abstract

A class of separable Banach sequence spaces is constructed. A member X of this class (i) is a hereditarily l¹ dual space which fails the Schur property, and (ii) is of codimension one in its first Baire class. A consequence of (ii) is that X is not isomorphic to the square of any Banach space Y .

Mathematical Subject Classification 2000

Primary: 46B20

Secondary: 46B25

Milestones

Received: 5 October 1984

Published: 1 April 1986