Schauder bases for symmetric tensor products
Grecu, Bogdan C.
Ryan, Raymond A.
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Grecu, Bogdan C. Ryan, Raymond A. (2005). Schauder bases for symmetric tensor products. Publications of the Research Institute for Mathematical Sciences 41 (2), 459-469
For a Banach space E with Schauder basis, we prove that the n fold symmetric tenser product (x) over cap (n)(mu,),E-s has a Schauder basis for all symmetric uniform crossnorms mu. This is done by modifying the square ordering on N-n and showing that the new ordering gives tensor product bases in both (x) over cap E-n(mu) and (x) over cap (n)(mu),E-s.