Bogdan Grecu Mathematics Department National University of Ireland Galway, Ireland E-mail address: bogdan@wuzwuz.nuigalway.ie

Schauder Bases for Symmetric Tensor Products

Abstract. For a Banach space E with Schauder basis, we prove that the n fold symmetric tensor product ˆ⊗_{μ, s}^{n}E has a Schauder basis for all symmetric uniform crossnorms μ. This is done by modifying the square ordering on ℕ^{n} and showing that the new ordering gives tensor product bases in both ˆ⊗_{μ}^{n}E and ˆ⊗_{μ, s}^{n}E.