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On the Maximal Operator Ideal Associated with a Tensor Norm Defined by Interpolation Spaces

  Published:2010-07-26
 Printed: Dec 2010
  • M. E. Puerta,
    Universidad EAFIT, Departamento de Ciencias B�icas, Medell�, Colombia
  • G. Loaiza,
    Universidad EAFIT, Departamento de Ciencias B�icas, Medell�, Colombia
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Abstract

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 and using $\ell_p$ 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.
Keywords: maximal operator ideals, ultraproducts of spaces, interpolation spaces maximal operator ideals, ultraproducts of spaces, interpolation spaces
MSC Classifications: 46M05, 46M35, 46A32 show english descriptions Tensor products [See also 46A32, 46B28, 47A80]
Abstract interpolation of topological vector spaces [See also 46B70]
Spaces of linear operators; topological tensor products; approximation properties [See also 46B28, 46M05, 47L05, 47L20]
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]
 

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