Vol. 46, No. 1, 1973

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A decomposition for B(X) and unique Hahn-Banach extensions

Julien O. Hennefeld

Vol. 46 (1973), No. 1, 197–199
Abstract

For a Banach space X, let B(X) be the space of all bounded linear operators on X, and 𝒞 the space of all compact linear operators on X. In general, the norm-pre-serving extension of a linear functional in the Hahn-Banach theorem is highly non-unique. The principal result of this paper is that, for X = c0 or lp with 1 < p < , each bounded linear functional on 𝒞 has a unique norm-preserving to B(X). This is proved by using a decomposition theorem for B(X), which takes on a special form for X = c0 or lp with 1 < p < .

Mathematical Subject Classification
Primary: 47D15
Secondary: 46B05
Milestones
Received: 15 December 1971
Published: 1 May 1973
Authors
Julien O. Hennefeld