Vol. 15, No. 3, 1965

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Projections in the space of bounded linear operators

David R. Arterburn and Robert James Whitley

Vol. 15 (1965), No. 3, 739–746

Thorp has shown that for X and Y certain Banach spaces of sequences there is no continuous linear projection of the bounded linear operators from X to Y onto the compact linear operators from X to Y . In this paper, this result, as well as related results for the weakly compact linear operators, is demonstrated for cases including (a) X an infinite dimensional abstract L-space and Y an infinite dimensional space whose conjugate contains a countable total set and (b) X a separable B-space and Y = C(S) with S either a metric space containing an infinite number of points or S a compact space which contains a one-to-one convergent sequence.

Mathematical Subject Classification
Primary: 47.10
Secondary: 46.10
Received: 11 August 1964
Published: 1 September 1965
David R. Arterburn
Robert James Whitley