On Banach spaces Y for which B(C(Ω),Y ) = K(C(Ω),Y )

Shamim Ismail Ansari

Vol. 169 (1995), No. 2, 201–218

DOI: 10.2140/pjm.1995.169.201

Abstract

Let Ω be a compact Hausdorff space. In this paper we give some necessary conditions and some sufficient conditions on a Banach space Y in order that all continuous linear operators from C(Ω) into Y are compact. We prove that for a nonscattered compact Hausdorff space Ω, for Y belonging to a large class of Banach spaces all operators from C(Ω) into Y are compact if and only if all operators from l² into Y are compact.

Mathematical Subject Classification 2000

Primary: 46B28

Secondary: 46B20, 46E15, 47B38

Milestones

Received: 10 December 1992

Published: 1 June 1995