A note on cones associated to Schauder bases |
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Authors: | Luis Rodríguez-Marín Miguel Sama |
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Institution: | (1) Departamento de Matemática Aplicada, E.T.S.I.I. Universidad Nacional de Educación a Distancia, Calle Juan del Rosal, 12, 28040 Madrid, Spain |
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Abstract: | We study the existence of infima of subsets in Banach spaces ordered by normal cones associated to shrinking Schauder bases.
Under these conditions we prove the existence of infima for a class of subsets verifying a weakly compactness property. Moreover
we prove that a normal cone associated to a Schauder basis in a reflexive Banach space is strongly minihedral extending the
known result for unconditional Schauder bases. Several examples are also discussed.
Miguel Sama: The work of this author is partially supported by Ministerio de Educación y Ciencia (Spain), project MTM2006-02629
and Ingenio Mathematica (i-MATH) CSD2006-00032 (ConsoliderIngenio 2010). |
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Keywords: | Ordered Banach spaces Schauder bases strongly minihedral cones |
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