Vol. 52, No. 2, 1974

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Projections in the spaces of bounded linear operations

Tsang Hai Kuo

Vol. 52 (1974), No. 2, 475–480

For Banach spaces X,Z, let B(X,Z) denote the space of bounded linear operators from X into Z and K(X,Z) (resp. W(X,Z)) the subspace of compact (resp. weakly compact) operators. It is shown that (a) if X contains an isomorph of c0, then K(X,l) is not complemented in B(X,l), (b) if S is a compact Hausdorff space which is not scattered, then K(C(S),Z) is not complemented in W(C(S),Z) for Z = c0 or l. In particular, K(l,c0) is not complemented in B(l,c0), which gives a negative answer to a question proposed by Arterburn and Whitley.

Mathematical Subject Classification
Primary: 46B05
Secondary: 47D15
Received: 15 August 1973
Revised: 21 January 1974
Published: 1 June 1974
Tsang Hai Kuo