On α-nuclearity and total accessibility for some tensor norms α
Keywords:α-nuclear operators, α-approximation property, totally accessible tensor norms, tensor products
For a tensor norm α on the class of all Banach spaces there is a natural way to define the Banach operator ideal Nα associated with the tensor norm. We give sufficient conditions for an operatorto be in Nα if its second adjoint posesses this property. We show one way to get from this the negative answers to some questions of A. Defant and K. Floret: their tensor norms g∞, w1 and w∞ are not totally accessible.