On α-nuclearity and total accessibility for some tensor norms α

Abstract

For a tensor norm α on the class of all Banach spaces there is a natural way to define the Banach operator ideal N_α associated with the tensor norm. We give sufficient conditions for an operatorto be in N_α  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.