The ordering structure on Banach spaces

Gerald Arthur Edgar and Jun Feng Zhao

Vol. 116 (1985), No. 2, 255–263

DOI: 10.2140/pjm.1985.116.255

Abstract

Suppose X, Y are Banach spaces. The binary relation X ≺ Y means X = ⋂ T^∗∗−1[Y ], where the intersection is taken over all bounded linear operators T : X → Y . We use this definition to study sums of Banach spaces and the spaces J(ω₁), C_[0,ω1].

Mathematical Subject Classification 2000

Primary: 46B20

Milestones

Received: 26 April 1983

Revised: 28 December 1983

Published: 1 February 1985