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

  • Sten Kaijser Uppsala University
  • Oleg Reinov St Petersburg University, Uppsala University
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.


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Author Biography

Sten Kaijser, Uppsala University

Department of Mathematics