Reinov, O.I.
On linear operators with p-nuclear adjoints.

Abstract:

If  p\in [1,+\infty] and  T is a linear operator
from a Banach space  X to a Banach space  Y, with
p-nuclear adjoint, then if one of the space  X^*
or  Y^{***} has the approximation property, then
T belongs to the ideal, dual to the ideal  N_p
of all  p-nuclear operators. On the other hand,
there is a Banach space  W, such that  W^{**} has
a basis, and so that for each  p\in [1,+\infty], p\neq 2,
there exists an operator  T: W^{**}\to W with
p-nuclear adjoint, which is not in the ideal, dual
to  N_p, as an operator from  W^{**} to  W.

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