Abstract
The J-sum of certain sequences of Banach spaces is defined and studied. This seems to be the first conditional sum studied in any detail. As applications for any weakly compactly generated Z, a concrete space X is constructed with X ââ X isometric to Z. Examples are constructed to show boundedly complete (even symmetric) decompositions (even with all the factors isometric to J) do not have the properties that boundedly complete bases have. A space X is constructed that is isomorphic to both X â and X ââ X . Of course, the J comes from James' quasi-reflexive space which this construction generalizes.
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