Canad. Math. Bull. 53(2010), 690-705
Printed: Dec 2010
The classical approach to studying operator ideals using tensor
norms mainly focuses on those tensor norms and operator ideals
defined by means of $\ell_p$ spaces. In a previous paper,
an interpolation space, defined via the real method
$\ell_p$ spaces, was used to define a tensor
norm, and the associated minimal operator ideals were characterized.
In this paper, the next natural step is taken, that is, the
corresponding maximal operator
ideals are characterized. As an application, necessary and sufficient
conditions for the coincidence of
the maximal and minimal ideals are given.
Finally, the previous results are used in order to find some new
metric properties of the mentioned tensor norm.
maximal operator ideals, ultraproducts of spaces, interpolation spaces
46M05 - Tensor products [See also 46A32, 46B28, 47A80]
46M35 - Abstract interpolation of topological vector spaces [See also 46B70]
46A32 - Spaces of linear operators; topological tensor products; approximation properties [See also 46B28, 46M05, 47L05, 47L20]