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On Lattice Summing Operators

1983
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Proceedings of the American Mathematical Society
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Given a Banach space E and a Banach lattice L, necessary and sufficient conditions on E and L are given such that every lattice summing operator T: E -L (cf. Introduction) is absolutely summing. 1. Introduction. The concept of absolutely summing operators has a certain natural analogue when the range space is a Banach lattice. Namely, an operator T: E -L is called lattice summing, if for every sequence (x") in E such that 1xn converges unconditionally, the series 2 | Txn | converges in L. Of

doi:10.2307/2043699
fatcat:v3w62quuo5ftrajblklf4f4hxe