Incompleteness of the linear span of the positive compact operators

Chen, Z.; Wickstead, A.

doi:10.1090/S0002-9939-97-04220-2

Incompleteness of the linear span of the positive compact operators
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by Z. L. Chen and A. W. Wickstead

Proc. Amer. Math. Soc. 125 (1997), 3381-3389

DOI: https://doi.org/10.1090/S0002-9939-97-04220-2

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Abstract:

We show that even in the case of a Banach lattice $E$ with an order continuous norm (or whose dual has an order continuous norm) the linear span of the positive compact operators on $E$ need not be complete under the regular norm.

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