Examinando por Materia "Ultraproducts of spaces"

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    On operator ideals defined by a reflexive Orlicz sequence space
    (Departamento de Matematicas, Universidad Catolica del Norte, 2006-01-01) López Molina, J.A.; Rivera, M.J.; Loaiza, G.; López Molina, J.A.; Rivera, M.J.; Loaiza, G.; Universidad EAFIT. Departamento de Ciencias; Matemáticas y Aplicaciones
    Classical theory of tensornorms and operator ideals studies mainly those defined by means of sequence spaces lp. Considering Orlicz sequence spaces as natural generalization of lp spaces, in a previous paper [12] an Orlicz sequence space was used to define a tensornorm, and characterize minimal and maximal operator ideals associated, by using local techniques. Now, in this paper we give a new characterization of the maximal operator ideal to continue our analysis of some coincidences among such operator ideals. Finally we prove some new metric properties of tensornorm mentioned above. © 2007 Universidad Católica del Norte, Departamento de Matemáticas.
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    On the Maximal Operator Ideal Associated with a Tensor Norm Defined by Interpolation Spaces
    (CANADIAN MATHEMATICAL SOC, 2010-12-01) Puerta, M. E.; Loaiza, G.; Puerta, M. E.; Loaiza, G.; Universidad EAFIT. Departamento de Ciencias; Matemáticas y Aplicaciones
    The classical approach to studying operator ideals using tensor norms mainly focuses on those tensor norms and operator ideals defined by means of `p spaces. In a previous paper, an interpolation space, defined via the real method and using `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. © Canadian Mathematical Society 2010.